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Wave-appropriate reconstruction of compressible flows: physics-constrained acoustic dissipation and rank-1 entropy wave correction
Authors:
Amareshwara Sainadh Chamarthi
Abstract:
The wave-appropriate reconstruction approach decomposes the reconstruction procedure into characteristic wave families, centralizing non-acoustic waves to minimize dissipation while retaining an upwind bias for acoustic waves. In previous implementations, the acoustic upwind parameter $η_a$ was fixed at its maximum value of $1.0$; however, this choice is conservative and motivated a systematic sea…
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The wave-appropriate reconstruction approach decomposes the reconstruction procedure into characteristic wave families, centralizing non-acoustic waves to minimize dissipation while retaining an upwind bias for acoustic waves. In previous implementations, the acoustic upwind parameter $η_a$ was fixed at its maximum value of $1.0$; however, this choice is conservative and motivated a systematic search for the minimum value that is robust across flow regimes. To this end, the CFD solver is treated as a black box within a bounded scalar minimization, which minimizes an accuracy objective for the subsonic inviscid TGV subject to a stability constraint enforced by the supersonic viscous TGV. Because the wave-appropriate framework leaves $η_a$ as the sole degree of freedom, the optimization converges in approximately 25 evaluations. The resulting optimal values generalize without retuning across a wide range from subsonic turbulence to hypersonic flows with shocks and contact discontinuities. The second contribution focuses on eliminating the need for an explicit contact-discontinuity detector, which is commonly required in flows involving both shock waves and contact discontinuities. In such cases, the reconstruction deficiency appears solely within the entropy characteristic wave and can be corrected by a rank-1 update along the entropy right eigenvector. The proposed algorithm relies only on the Ducros sensor and is limiter-agnostic, facilitating direct use in other schemes, such as WENO. This approach reduces wall time by $29$--$41\%$ compared to full characteristic decomposition. To further demonstrate the method's generality, introducing a controlled acoustic bias exclusively to the normal momentum in a KEP scheme eliminates spurious vortices in periodic shear layers, confirming that the acoustic stability mechanism operates independently of the discretization framework.
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Submitted 6 April, 2026; v1 submitted 3 April, 2026;
originally announced April 2026.
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Assessment of Gradient-based Reconstruction and Artificial Diffusivity Methods in Simulating High-Speed Compressible Flows
Authors:
R. R. Kumar,
S. Saini,
N. R. Vadlamani,
A. S. Chamarthi
Abstract:
The two promising methods for capturing high-speed flows are local artificial diffusivity (LAD) and centralised gradient-based reconstruction (C-GBR), the former being computationally economical and the latter being more robust and stable but expensive. While the LAD approach captures discontinuities by adding artificial fluid transport coefficients, C-GBR employs a wave appropriate discontinuity…
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The two promising methods for capturing high-speed flows are local artificial diffusivity (LAD) and centralised gradient-based reconstruction (C-GBR), the former being computationally economical and the latter being more robust and stable but expensive. While the LAD approach captures discontinuities by adding artificial fluid transport coefficients, C-GBR employs a wave appropriate discontinuity sensor to obtain cleaner results and utilises the HLLC approximate Riemann solver for computing inviscid fluxes. The efficacy of these schemes is initially demonstrated in single-species 1D and 2D test cases. Moreover, the shock-capturing capability is assessed for 3D supersonic and hypersonic turbulent boundary layers. The accuracy of LAD predictions is comparable to that of C-GBR for the test case of a supersonic turbulent boundary layer. From the stability front, all simulations are found to be stable with the C-GBR scheme, whereas the LAD-based simulations are observed to abruptly diverge for supersonic and hypersonic flows over compression corners with stronger shocks and larger flow separations. From the computational front, the LAD-based schemes are $1.17 - 2.32 \times$ faster than the monotonicity-preserving explicit/implicit C-GBR schemes. A hybrid approach leveraging the strengths of LAD and GBR schemes is proposed as a promising solution for high-speed turbulent flows with strong shock-boundary layer interactions. The efficacy of the hybrid LAD-GBR solver is demonstrated for the compressible triple-point and supersonic compression ramp test cases. For the M2.9, $24^{\circ}$ case, the hybrid solver was stable and achieved a notable $1.67 \times$ speed-up over the C-GBR scheme.
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Submitted 22 November, 2025;
originally announced November 2025.
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viper: High-precision radial velocities from the optical to the infrared (Reaching 3 m/s in the K band of CRIRES+ with telluric modelling)
Authors:
J. Köhler,
M. Zechmeister,
A. Hatzes,
S. Chamarthi,
E. Nagel,
U. Seemann,
P. Ballester,
P. Bristow,
P. Chaturvedi,
R. J. Dorn,
E. Guenther,
V. D. Ivanov,
Y. Jung,
O. Kochukhov,
T. Marquart,
L. Nortmann,
R. Palsa,
N. Piskunov,
A. Reiners,
F. Rodler,
J. V. Smoker
Abstract:
In recent years, a number of new instruments and data reduction pipelines have been developed to obtain high-precision radial velocities (RVs). In particular in the optical, considerable progress has been made and RV precision below 50 cm/s has been reached. Yet, the RV precision in the near-infrared (NIR) is trailing behind. This is due to a number of factors, such as imprinted atmospheric absorp…
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In recent years, a number of new instruments and data reduction pipelines have been developed to obtain high-precision radial velocities (RVs). In particular in the optical, considerable progress has been made and RV precision below 50 cm/s has been reached. Yet, the RV precision in the near-infrared (NIR) is trailing behind. This is due to a number of factors, such as imprinted atmospheric absorption lines, lower stellar information content, different types of detectors, and usable calibration lamps. However, observations in the NIR are important for the search and study of exoplanets around cool low-mass stars that are faint at optical wavelengths. Not only are M dwarfs brightest in the NIR, the signal of stellar activity is also reduced at longer wavelengths. In this paper we introduce the RV pipeline viper (Velocity and IP EstimatoR). The philosophy of viper is to offer a publicly available and user-friendly code that is able to process data from various spectrographs. Originally designed to handle data from optical instruments, the code now has been extended to enable the processing of NIR data. viper uses a least-square fitting to model the stellar RV as well as the temporal and spatial variable IP. We have improved upon this method by adding a term for the telluric spectrum that enables the forward modelling of molecules present in the Earth's atmosphere. In this paper we use CRIRES+ observations in the K band to demonstrate viper's ability to handle data in the NIR. We show that it is possible to achieve an RV accuracy of 3 m/s over a period of 2.5 years with the use of a gas cell. Additionally, we present a study of the stability of atmospheric lines in the NIR. With viper it is possible to handle data taken with or without a gas cell, and we show that a long-term RV precision of around 10 m/s can be achieved when using only telluric lines for the wavelength calibration.
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Submitted 13 May, 2025;
originally announced May 2025.
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Wave or Physics-Appropriate Multidimensional Upwinding Approach for Compressible Multiphase Flows
Authors:
Amareshwara Sainadh Chamarthi
Abstract:
This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm applies different reconstruction schemes to acoustic, vorticity, and entropy waves in characteristic space to enhance accuracy and minimize numerical artifacts. In ch…
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This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm applies different reconstruction schemes to acoustic, vorticity, and entropy waves in characteristic space to enhance accuracy and minimize numerical artifacts. In characteristic space, upwind schemes are used for acoustic waves, central schemes for vorticity and entropy waves, and Tangent of Hyper-bola for INterface Capturing (THINC) reconstruction for material interfaces and contact discontinuities (a subset of entropy waves). This approach prevents spurious vortices in periodic shear layers, accurately captures vortical structures in gas-gas and gas-liquid interactions, and improves the accuracy of shock-entropy wave interactions. In physical space, phasic densities are computed using THINC in regions of contact discontinuities and material interfaces, while tangential velocities are calculated with central schemes to improve vortical structures. An adaptive reconstruction technique is also introduced to mitigate oscillations near shocks, which arise from primitive variable reconstruction, by combining primitive and characteristic variable reconstructions with the liquid phase being identified using the stiffened gas parameter. The proposed multidimensional upwinding approach outperforms traditional schemes, demonstrating superior accuracy in capturing physical phenomena, reducing numerical artifacts, and better matching experimental results across complex test cases.
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Submitted 4 January, 2025;
originally announced January 2025.
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Consistent Interface Capturing Adaptive Reconstruction Approach for Viscous Compressible Multicomponent Flows
Authors:
Amareshwara Sainadh Chamarthi
Abstract:
The paper proposes a physically consistent numerical discretization approach for simulating viscous compressible multicomponent flows. It has two main contributions. First, a contact discontinuity (and material interface) detector is developed. In those regions of contact discontinuities, the THINC (Tangent of Hyperbola for INterface Capturing) approach is used for reconstructing appropriate varia…
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The paper proposes a physically consistent numerical discretization approach for simulating viscous compressible multicomponent flows. It has two main contributions. First, a contact discontinuity (and material interface) detector is developed. In those regions of contact discontinuities, the THINC (Tangent of Hyperbola for INterface Capturing) approach is used for reconstructing appropriate variables (phasic densities). For other flow regions, the variables are reconstructed using the Monotonicity-preserving (MP) scheme (or Weighted essentially non-oscillatory scheme (WENO)). For reconstruction in the characteristic space, the THINC approach is used only for the contact (or entropy) wave and volume fractions and for the reconstruction of primitive variables, the THINC approach is used for phasic densities and volume fractions only, offering an effective solution for reducing dissipation errors near contact discontinuities. The second contribution is the development of an algorithm that uses a central reconstruction scheme for the tangential velocities, as they are continuous across material interfaces in viscous flows. In this regard, the Ducros sensor (a shock detector that cannot detect material interfaces) is employed to compute the tangential velocities using a central scheme across material interfaces. Using the central scheme does not produce any oscillations at the material interface. The proposed approach is thoroughly validated with several benchmark test cases for compressible multicomponent flows, highlighting its advantages. The numerical results of the benchmark tests show that the proposed method captured the material interface sharply compared to existing methods.
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Submitted 7 January, 2025; v1 submitted 29 October, 2024;
originally announced October 2024.
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A generalized adaptive central-upwind scheme for compressible flow simulations and preventing spurious vortices
Authors:
Amareshwara Sainadh Chamarthi
Abstract:
This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the central gradient-based reconstruction approach presented in [1] (Hoffmann, Chamarthi and Frankel, JCP 2024). By leveraging a combination of conservative and character…
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This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the central gradient-based reconstruction approach presented in [1] (Hoffmann, Chamarthi and Frankel, JCP 2024). By leveraging a combination of conservative and characteristic variable reconstruction, the proposed approach demonstrates oscillation-free results while effectively reducing computational costs and improving the results. Furthermore, the adaptive central-upwind algorithm is generalized to be compatible not only with the gradient-based reconstruction as in [1] but with other existing methods. In this regard, with the proposed algorithm, the standard fifth/sixth-order reconstruction scheme has also been shown to outperform existing schemes with a 20-30% reduction in computational expense with improved results. Notably, the proposed approach has successfully prevented the generation of spurious vortices in the double shear layer test cases, even with linear schemes, showcasing its robustness and effectiveness.
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Submitted 3 September, 2024;
originally announced September 2024.
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Centralized Gradient-Based Reconstruction for Wall Modelled Large Eddy Simulations of Hypersonic Boundary Layer Transition
Authors:
Natan Hoffmann,
Amareshwara Sainadh Chamarthi,
Steven H. Frankel
Abstract:
In this study, we introduce a robust central Gradient-Based Reconstruction (GBR) scheme for the compressible Navier-Stokes equations. The method leverages transformation to characteristic space, allowing selective treatment of waves from the compressible Euler equations. By averaging left- and right-biased state interpolations, a central scheme is achieved for all but the acoustic waves, which req…
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In this study, we introduce a robust central Gradient-Based Reconstruction (GBR) scheme for the compressible Navier-Stokes equations. The method leverages transformation to characteristic space, allowing selective treatment of waves from the compressible Euler equations. By averaging left- and right-biased state interpolations, a central scheme is achieved for all but the acoustic waves, which require upwinding for stability. Distinct differences were observed between transformations using either primitive or conservative variables. We evaluated the method's robustness and superiority using benchmark problems, including the two-dimensional shock entropy problem, two-dimensional viscous shock tube, and three-dimensional inviscid Taylor-Green vortex. Subsequently, we assessed the method in the context of Wall Modelled Large Eddy Simulations (WMLES), where coarse grids are used to reduce computational cost but also introduce substantial numerical dissipation. Using WMLES, we simulated oblique shock impingement on a Mach 6 disturbed boundary layer and a Mach 7.7 flow over a $15^{\circ}$ compression ramp. Our findings reveal that: 1) transformation to characteristic space using conservative variables leads to more accurate results; 2) minimizing numerical dissipation through centralized interpolation is crucial. In the compression ramp case, boundary layer separation was shifted slightly upstream, and there was an over-prediction of wall heating, likely attributable to the equilibrium-assuming wall model. Overall, this work showcases the method's potential in accurately capturing complex flow dynamics with reduced numerical dissipation.
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Submitted 18 May, 2024;
originally announced May 2024.
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Mitigating the Influence of Domain Shift in Skin Lesion Classification: A Benchmark Study of Unsupervised Domain Adaptation Methods on Dermoscopic Images
Authors:
Sireesha Chamarthi,
Katharina Fogelberg,
Roman C. Maron,
Titus J. Brinker,
Julia Niebling
Abstract:
The potential of deep neural networks in skin lesion classification has already been demonstrated to be on-par if not superior to the dermatologists diagnosis. However, the performance of these models usually deteriorates when the test data differs significantly from the training data (i.e. domain shift). This concerning limitation for models intended to be used in real-world skin lesion classific…
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The potential of deep neural networks in skin lesion classification has already been demonstrated to be on-par if not superior to the dermatologists diagnosis. However, the performance of these models usually deteriorates when the test data differs significantly from the training data (i.e. domain shift). This concerning limitation for models intended to be used in real-world skin lesion classification tasks poses a risk to patients. For example, different image acquisition systems or previously unseen anatomical sites on the patient can suffice to cause such domain shifts. Mitigating the negative effect of such shifts is therefore crucial, but developing effective methods to address domain shift has proven to be challenging. In this study, we carry out an in-depth analysis of eight different unsupervised domain adaptation methods to analyze their effectiveness in improving generalization for dermoscopic datasets. To ensure robustness of our findings, we test each method on a total of ten distinct datasets, thereby covering a variety of possible domain shifts. In addition, we investigated which factors in the domain shifted datasets have an impact on the effectiveness of domain adaptation methods. Our findings show that all of the eight domain adaptation methods result in improved AUPRC for the majority of analyzed datasets. Altogether, these results indicate that unsupervised domain adaptations generally lead to performance improvements for the binary melanoma-nevus classification task regardless of the nature of the domain shift. However, small or heavily imbalanced datasets lead to a reduced conformity of the results due to the influence of these factors on the methods performance.
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Submitted 5 October, 2023;
originally announced October 2023.
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A Wave Appropriate Discontinuity Sensor Approach for Compressible Flows
Authors:
Amareshwara Sainadh Chamarthi,
Natan Hoffmann,
Steven Frankel
Abstract:
In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce high-frequency oscillations during interpolation to cell interfaces, we exploit the characteristic wave structure of the Euler equations to selectively treat the various wa…
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In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce high-frequency oscillations during interpolation to cell interfaces, we exploit the characteristic wave structure of the Euler equations to selectively treat the various waves that the equations comprise. The approach uses the Ducros shock sensing criterion to detect and limit oscillations due to shocks while applying a different criterion to detect and limit oscillations due to contact discontinuities. Furthermore, the method is general in the sense that it can be applied to any method that employs characteristic transformation and shock sensors. However, in the present work, we focus on the Gradient-Based Reconstruction family of schemes. A series of inviscid and viscous test cases containing various types of discontinuities are carried out. The proposed method is shown to markedly reduce high-frequency oscillations that arise due to improper treatment of the various discontinuities; i.e., applying the Ducros shock sensor in a flow where a strong contact discontinuity is present. Moreover, the proposed method is shown to predict similar volume-averaged kinetic energy and enstrophy profiles for the Taylor-Green vortex simulation compared to the base Ducros sensor, indicating that it does not introduce unnecessary numerical dissipation when there are no contact discontinuities in the flow.
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Submitted 15 May, 2023;
originally announced May 2023.
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Efficient high-order Gradient-based Reconstruction for compressible flows
Authors:
Amareshwara Sainadh Chamarthi
Abstract:
This paper extends the gradient-based reconstruction approach of Chamarthi \cite{chamarthi2023gradient} to genuine high-order accuracy for inviscid test cases involving smooth flows. A seventh-order accurate scheme is derived using the same stencil as of the explicit fourth-order scheme proposed in Ref. \cite{chamarthi2023gradient}, which also has low dissipation properties. The proposed method is…
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This paper extends the gradient-based reconstruction approach of Chamarthi \cite{chamarthi2023gradient} to genuine high-order accuracy for inviscid test cases involving smooth flows. A seventh-order accurate scheme is derived using the same stencil as of the explicit fourth-order scheme proposed in Ref. \cite{chamarthi2023gradient}, which also has low dissipation properties. The proposed method is seventh-order accurate under the assumption that the variables at the \textit{cell centres are point values}. A problem-independent discontinuity detector is used to obtain high-order accuracy. Accordingly, primitive or conservative variable reconstruction is performed around regions of discontinuities, whereas smooth solution regions apply flux reconstruction. The proposed approach can still share the derivatives between the inviscid and viscous fluxes, which is the main idea behind the gradient-based reconstruction. Several standard benchmark test cases are presented. The proposed method is more efficient than the seventh-order weighted compact nonlinear scheme (WCNS) for the test cases considered in this paper.
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Submitted 1 May, 2023;
originally announced May 2023.
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Domain shifts in dermoscopic skin cancer datasets: Evaluation of essential limitations for clinical translation
Authors:
Katharina Fogelberg,
Sireesha Chamarthi,
Roman C. Maron,
Julia Niebling,
Titus J. Brinker
Abstract:
The limited ability of Convolutional Neural Networks to generalize to images from previously unseen domains is a major limitation, in particular, for safety-critical clinical tasks such as dermoscopic skin cancer classification. In order to translate CNN-based applications into the clinic, it is essential that they are able to adapt to domain shifts. Such new conditions can arise through the use o…
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The limited ability of Convolutional Neural Networks to generalize to images from previously unseen domains is a major limitation, in particular, for safety-critical clinical tasks such as dermoscopic skin cancer classification. In order to translate CNN-based applications into the clinic, it is essential that they are able to adapt to domain shifts. Such new conditions can arise through the use of different image acquisition systems or varying lighting conditions. In dermoscopy, shifts can also occur as a change in patient age or occurence of rare lesion localizations (e.g. palms). These are not prominently represented in most training datasets and can therefore lead to a decrease in performance. In order to verify the generalizability of classification models in real world clinical settings it is crucial to have access to data which mimics such domain shifts. To our knowledge no dermoscopic image dataset exists where such domain shifts are properly described and quantified. We therefore grouped publicly available images from ISIC archive based on their metadata (e.g. acquisition location, lesion localization, patient age) to generate meaningful domains. To verify that these domains are in fact distinct, we used multiple quantification measures to estimate the presence and intensity of domain shifts. Additionally, we analyzed the performance on these domains with and without an unsupervised domain adaptation technique. We observed that in most of our grouped domains, domain shifts in fact exist. Based on our results, we believe these datasets to be helpful for testing the generalization capabilities of dermoscopic skin cancer classifiers.
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Submitted 3 July, 2023; v1 submitted 14 April, 2023;
originally announced April 2023.
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On the Application of Gradient Based Reconstruction for Flow Simulations on Generalized Curvilinear and Dynamic Mesh Domains
Authors:
Hemanth Chandravamsi,
Amareshwara Sainadh Chamarthi,
Natan Hoffmann,
Steven H. Frankel
Abstract:
Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and $α$-damping schemes introduced by Chamarthi (2022) [1] for simulating high-speed flows in generalized curvilinear and dynamic mesh domains with the freestream preservatio…
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Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and $α$-damping schemes introduced by Chamarthi (2022) [1] for simulating high-speed flows in generalized curvilinear and dynamic mesh domains with the freestream preservation property. In the first part of this paper, the algorithms are detailed within the generalized curvilinear coordinate framework, with a focus on demonstration through stationary and dynamic mesh test cases. It has been shown both theoretically and through the use of test cases that the conservative metrics, including their interpolation to cell interfaces, must be numerically computed using a central scheme that is consistent with the inviscid flux algorithm to achieve the freestream preservation property. The second part of the paper illustrates the efficacy of the algorithm in simulating supersonic jet screech by displaying its capability to capture the screech tones and accurately characterize the unsteady lateral flapping mode of a Mach 1.35 under-expanded supersonic jet, in contrast to the WENO-Z scheme which fails to do so at the same grid resolution. In the final part of the paper, the parallelizability of the schemes on GPU architectures is demonstrated and performance metrics are evaluated. A significant speedup of over $200 \times$ (compared to a single core CPU) and a reduction in simulation completion time to 34.5 hours per simulation were achieved for the supersonic jet noise case at a grid resolution of 13 million cells.
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Submitted 19 March, 2023;
originally announced March 2023.
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On the role of spectral properties of viscous flux discretization for flow simulations on marginally resolved grids
Authors:
Amareshwara Sainadh Chamarthi,
Hemanth Chandra Vamsi K,
Natan Hoffmann,
Sean Bokor,
Steven H. Frankel
Abstract:
In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different classes, with poor and better representation of spectral properties at high wavenumbers. Both theoretical and numerical results have revealed that the method with…
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In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different classes, with poor and better representation of spectral properties at high wavenumbers. Both theoretical and numerical results have revealed that the method with better properties at high wavenumbers, denoted as $α$-damping type discretization, produced superior solutions compared to the other class of methods. The proposed compact $α$-damping method converged towards the direct numerical simulation (DNS) solution at lower grid resolution compared with the other class of methods and is, therefore, a better candidate for high fidelity large-eddy simulations (LES) and DNS studies.
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Submitted 29 November, 2022; v1 submitted 29 June, 2022;
originally announced June 2022.
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Gradient Based Reconstruction: Inviscid and viscous flux discretizations, shock capturing, and its application to single and multicomponent flows
Authors:
Amareshwara Sainadh Chamarthi
Abstract:
This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative sharing between the inviscid and viscous schemes: highly accurate explicit and implicit gradients are used for the solution reconstruction expressed in terms of deriv…
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This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative sharing between the inviscid and viscous schemes: highly accurate explicit and implicit gradients are used for the solution reconstruction expressed in terms of derivatives. The higher-order accurate gradients of the velocity components are reused to compute the viscous fluxes for efficiency and significantly improve the solution and gradient quality, as demonstrated by several viscous-flow test cases. The viscous schemes are fourth-order accurate and carefully designed with a high-frequency damping property, which has been identified as a critically important property for stable compressible-flow simulations with shock waves [Chamarthi et al., JCP, 2022]. Shocks and material discontinuities are captured using a monotonicity-preserving (MP) scheme, which is also improved by reusing the gradients. For inviscid test cases, The proposed scheme is fourth-order for linear and second-order accurate for non-linear problems. Several numerical results obtained for simulations of complex viscous flows are presented to demonstrate the accuracy and robustness of the proposed methodology.
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Submitted 28 October, 2022; v1 submitted 2 May, 2022;
originally announced May 2022.
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On the Importance of High-Frequency Damping in High-Order Conservative Finite-Difference Schemes for Viscous Fluxes
Authors:
Amareshwara Sainadh Chamarthi,
Sean Bokor,
Steven H. Frankel
Abstract:
This paper discusses the importance of high-frequency damping in high-order conservative finite-difference schemes for viscous terms in the Navier-Stokes equations. Investigating nonlinear instability encountered in a high-resolution viscous shock-tube simulation, we have discovered that a modification to the viscous scheme rather than the inviscid scheme resolves a problem with spurious oscillati…
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This paper discusses the importance of high-frequency damping in high-order conservative finite-difference schemes for viscous terms in the Navier-Stokes equations. Investigating nonlinear instability encountered in a high-resolution viscous shock-tube simulation, we have discovered that a modification to the viscous scheme rather than the inviscid scheme resolves a problem with spurious oscillations around shocks. The modification introduces a term responsible for high-frequency damping that is missing in a conservative high-order viscous scheme. The importance of damping has been known for schemes designed for unstructured grids. However, it has not been recognized well in very high-order difference schemes, especially in conservative difference schemes. Here, we discuss how it is easily missed in a conservative scheme and how to improve such schemes by a suitably designed damping term.
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Submitted 1 April, 2022;
originally announced April 2022.
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Implicit gradients based conservative numerical scheme for compressible flows
Authors:
Amareshwara Sainadh Chamarthi,
Natan Hoffmann,
Hiroaki Nishikawa,
Steven H. Frankel
Abstract:
This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by compact finite differences, referred to as implicit gradients in this paper. A problem-independent shock capturing approach via Boundary Va…
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This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by compact finite differences, referred to as implicit gradients in this paper. A problem-independent shock capturing approach via Boundary Variation Diminishing (BVD) algorithm is used to suppress oscillations for the simulation of flows with shocks and material interfaces. Several numerical test cases are carried out to verify the proposed method's capability using the implicit gradient method for compressible flows.
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Submitted 10 February, 2023; v1 submitted 11 October, 2021;
originally announced October 2021.
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Discovery of an inflated hot Jupiter around a slightly evolved star TOI-1789
Authors:
Akanksha Khandelwal,
Priyanka Chaturvedi,
Abhijit Chakraborty,
Rishikesh Sharma,
Eike. W. Guenther,
Carina M. Persson,
Malcolm Fridlund,
Artie P. Hatzes,
Neelam J. S. S. V. Prasad,
Massimiliano Esposito,
Sireesha Chamarthi,
Ashirbad Nayak,
Dishendra,
Steve B. Howell
Abstract:
We report here the discovery of a hot Jupiter at an orbital period of $3.208666\pm0.000016$ days around TOI-1789 (TYC 1962-00303-1, $TESS_{mag}$ = 9.1) based on the TESS photometry, ground-based photometry, and high-precision radial velocity observations. The high-precision radial velocity observations were obtained from the high-resolution spectrographs, PARAS at Physical Research Laboratory (PRL…
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We report here the discovery of a hot Jupiter at an orbital period of $3.208666\pm0.000016$ days around TOI-1789 (TYC 1962-00303-1, $TESS_{mag}$ = 9.1) based on the TESS photometry, ground-based photometry, and high-precision radial velocity observations. The high-precision radial velocity observations were obtained from the high-resolution spectrographs, PARAS at Physical Research Laboratory (PRL), India, and TCES at Thüringer Landessternwarte Tautenburg (TLS), Germany, and the ground-based transit observations were obtained using the 0.43~m telescope at PRL with the Bessel-$R$ filter. The host star is a slightly evolved ($\log{g_*}$ = $3.939^{+0.024}_{-0.046}$), late F-type ($T_{eff}$ = $5984^{+55}_{-57}$ K), metal-rich star ([Fe/H] = $0.370^{+0.073}_{-0.089}$ dex) with a radius of {\ensuremath{$R_{*}$}} = $2.172^{+0.037}_{-0.035}$ \(R_\odot\) located at a distance of $223.56^{+0.91}_{-0.90}$ pc. The simultaneous fitting of the multiple light curves and the radial velocity data of TOI-1789 reveals that TOI-1789b has a mass of $M_{P}$ = $0.70\pm0.16 $ $M_{J}$, a radius of $R_{P}$ = $1.40^{+0.22}_{-0.13}$ $R_{J}$, and a bulk density of $ρ_P$ = $0.31^{+0.15}_{-0.13}$ g cm$^{-3}$ with an orbital separation of a = $0.04873^{+0.00065}_{-0.0016}$ AU. This puts TOI-1789b in the category of inflated hot Jupiters. It is one of the few nearby evolved stars with a close-in planet. The detection of such systems will contribute to our understanding of mechanisms responsible for inflation in hot Jupiters and also provide an opportunity to understand the evolution of planets around stars leaving the main sequence branch.
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Submitted 9 October, 2021; v1 submitted 16 June, 2021;
originally announced June 2021.
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Implicit gradients based novel finite volume scheme for compressible single and multi-component flows
Authors:
Amareshwara Sainadh Chamarthi,
Steven H. Frankel,
Abhishek Chintagunta
Abstract:
This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries in the finite volume approach. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by compact finite differences, referred to as implicit gradients in this paper. The new finite volume scheme has superior dispersion and dissipation properties in…
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This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries in the finite volume approach. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by compact finite differences, referred to as implicit gradients in this paper. The new finite volume scheme has superior dispersion and dissipation properties in comparison to the compact reconstruction approach. These implicit gradients are re-used in viscous flux computation and post-processing, which further improves efficiency. A problem-independent shock capturing approach via Boundary Variation Diminishing (BVD) algorithm is used to suppress oscillations for the simulation of flows with shocks and material interfaces. Several numerical test cases are carried out to verify the proposed finite volume method's capability using the implicit gradient method for single and multicomponent flows. Significant improvements are observed by computing the gradients implicitly for the viscous flows.
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Submitted 3 June, 2021;
originally announced June 2021.
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High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm
Authors:
Amareshwara Sainadh Chamarthi,
Steven Frankel
Abstract:
In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shock-capturing based on a boundary variation diminishing (BVD) reconstruction. In our approach, we combine a non-dissipative sixth-order central compact interpolation and a fifth-order monotonicity preserving scheme (MP5) through the BVD algorithm. For a smooth solution, the BVD reconstruction chooses the highest order…
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In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shock-capturing based on a boundary variation diminishing (BVD) reconstruction. In our approach, we combine a non-dissipative sixth-order central compact interpolation and a fifth-order monotonicity preserving scheme (MP5) through the BVD algorithm. For a smooth solution, the BVD reconstruction chooses the highest order possible interpolation, which is central, i.e. non-dissipative in the current approach and for the discontinuities, the algorithm selects the monotone scheme. This method provides an alternative to the existing adaptive upwind-central schemes in the literature. Several numerical examples are conducted with the present approach, which suggests that the current method is capable of resolving small scale flow features and has the same ability to capture sharp discontinuities as the MP5 scheme.
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Submitted 17 December, 2020;
originally announced December 2020.
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First order hyperbolic approach for Anisotropic Diffusion equation
Authors:
Amareshwara Sainadh Chamarthi,
Hiroaki Nishikawa,
Kimiya Komurasaki
Abstract:
In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate fifth-order scheme that is independent of the degree of anisotropy is made straightforward by the hyperbolic method with an optimal length scale. We demonstrate that the grad…
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In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate fifth-order scheme that is independent of the degree of anisotropy is made straightforward by the hyperbolic method with an optimal length scale. We demonstrate that the gradients are computed simultaneously to the same order of accuracy as that of the solution variable by using weight compact finite difference schemes. Furthermore, the approach is extended to improve further the simulation of the magnetized electrons test case previously discussed in Refs.[J. Comput. Phys., 284 (2015) 59-69 and 374 (2018) 1120-1151]. Numerical results indicate that these schemes are capable of delivering high accuracy and the proposed approach is expected to allow the hyperbolic method to be successfully applied to a wide variety of linear and nonlinear problems with anisotropic diffusion.
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Submitted 27 July, 2019;
originally announced July 2019.
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Estimation and correction of the instrumental perturbations of Vainu Bappu Telescope Echelle spectrograph using a model-based approach
Authors:
Sireesha Chamarthi,
Ravinder K. Banyal,
Sriram Sripadmanabhan
Abstract:
The Echelle spectrograph operating at Vainu Bappu Telescope (VBT), India, is a general purpose instrument used for many high-resolution spectroscopic observations. A concerted effort is being made to expand the scientific capability of the instrument in emerging areas of observational astronomy. The present study is aimed at evaluating the feasibility of the spectrograph to carry out precision Rad…
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The Echelle spectrograph operating at Vainu Bappu Telescope (VBT), India, is a general purpose instrument used for many high-resolution spectroscopic observations. A concerted effort is being made to expand the scientific capability of the instrument in emerging areas of observational astronomy. The present study is aimed at evaluating the feasibility of the spectrograph to carry out precision Radial Velocity (RV) measurements. In the current design, major factors limiting the RV precision of the spectrograph arise from the movable grating and slit; optical aberrations; positional uncertainty associated with optomechanical mounts and environmental and thermal instabilities in the spectrograph room. RV instabilities due to temperature and pressure variations in the environment are estimated to vary around 120 $ \textrm{ms}^{-1} $ and 400 $ \textrm{ms}^{-1} $ respectively. The positional uncertainty of the grating in the spectrograph could induce a spectral shift $\sim1.4\,\textrm{kms}^{-1} $ across the Echelle orders. A Zemax model is used to overcome the uncertainty in the zero-positioning and lack of repeatability of the moving components. We propose to obtain the ThAr lamp observations and using the Zemax model as the reference, predict the drifts in the positions of the optical components. The perturbations of the optical components from the nominal position are corrected at the beginning of the observational run. After a good match is obtained between the model and the observations, we propose to use a Zemax model to improve the wavelength calibration solution. We could match the observations and model within $\pm$~1 pixels accuracy after the model parameters were perturbed in a real-time setup of the spectrograph. In this paper, we present the estimation of the perturbations of optical components and the effect on the RV obtained.
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Submitted 12 June, 2019;
originally announced June 2019.
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Toward precision radial velocity measurements using Echelle spectrograph at Vainu Bappu Telescope
Authors:
Sireesha Chamarthi,
Ravinder K. Banyal,
S. Sriram
Abstract:
The Echelle spectrograph operating at Vainu Bappu Telescope (VBT) is a general purpose instrument designed for high resolution spectroscopy. It is being considered for precision Doppler measurements without altering the existing design and basic usage. However, the design level limitations and environmental perturbations are a major source of instability and systematic errors. As a result, a small…
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The Echelle spectrograph operating at Vainu Bappu Telescope (VBT) is a general purpose instrument designed for high resolution spectroscopy. It is being considered for precision Doppler measurements without altering the existing design and basic usage. However, the design level limitations and environmental perturbations are a major source of instability and systematic errors. As a result, a small Doppler signal in the stellar spectra is completely swamped by the large and uncontrolled instrumental drift. In this paper, we discuss some of the remedial measures we took to improve the radial velocity performance of the spectrograph. We show that a new auto-guider assembly has greatly reduced the mechanical jitter of the star image at the fibre input, making the illumination of the spectrograph slit at the other end stable. We have also installed an iodine absorption cell to track and eliminate the instrumental drifts to facilitate precision radial velocity observations. Furthermore, we have developed a generic algorithm that uses iodine exposures to extract the stellar radial velocities without the need for the complex forward modeling. Our algorithm is not accurate to the level of traditional iodine technique. However it is convenient to use on a low-cost general-purpose spectrograph targeting a moderate Radial Velocity (RV) precision at a few 10-100~$\textrm{ms}^{-1}$ level. Finally, we have demonstrated the usefulness of our approach by measuring the RV signal of a well known short-period, planet-hosting star.
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Submitted 25 May, 2019;
originally announced May 2019.
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High-order upwind and non-oscillatory approach for steady state diffusion, advection-diffusion and application to magnetized electrons
Authors:
Amareshwara Sainadh Chamarthi,
Kimiya Komurasaki,
Rei Kawashima
Abstract:
Steady state simulations} of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially non-oscillatory (WENO). Along with the magnetized electrons, the diffusion equation is also simulated to demonstrate the implementation and design order of the…
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Steady state simulations} of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially non-oscillatory (WENO). Along with the magnetized electrons, the diffusion equation is also simulated to demonstrate the implementation and design order of the accuracy of the approach due to their similar upwind structure. We show the adequacy of linear upwind schemes for diffusion equation and the use of shock-capturing scheme like WENO does not have any adverse effect on the solution, unlike the total-variation diminishing (TVD) methods. We further extended the approach to advection-diffusion equation, and appropriate boundary conditions have obtained a consistent design accuracy of the third and fifth order. We implemented the WENO approach to advection-diffusion equation by using the split hyperbolic method to demonstrate the advantage of non-oscillatory schemes to capture sharp gradients in boundary layer type problems without spurious oscillations. Finally, numerical results for magnetized electrons simulations indicate that with increasing strength of magnetic confinement it is possible to capture sharp gradients without oscillations by WENO scheme.
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Submitted 8 March, 2019;
originally announced March 2019.
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Stability analysis of VBT Echelle spectrograph for precise radial velocity measurements
Authors:
Sireesha Chamarthi,
Ravinder K. Banyal,
S. Sriram,
Gajendra Pandey
Abstract:
A fiber-fed Echelle spectrograph at 2.3 m Vainu Bappu Telescope (VBT), Kavalur, has been in operation since 2005. Owing to various technological advancements in precision spectroscopy in recent years, several research avenues have been opened in observational astronomy. These developments have created a demand to improve the Doppler precision of our spectrograph. Currently, the stability of the in…
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A fiber-fed Echelle spectrograph at 2.3 m Vainu Bappu Telescope (VBT), Kavalur, has been in operation since 2005. Owing to various technological advancements in precision spectroscopy in recent years, several research avenues have been opened in observational astronomy. These developments have created a demand to improve the Doppler precision of our spectrograph. Currently, the stability of the instrument is compromised by the temperature and pressure fluctuations inside the Echelle room. Further, a better wavelength calibration approach is needed to carefully track and disentangle the instrumental effects from stellar spectra. While planning a possible upgrade with an Iodine absorption gas cell, we measured the raw stability of the spectrograph using a series of calibration frames taken with the ThAr gas discharge lamp. The time series data were analysed with cross-correlation method and the shift in ThAr emission lines was accurately measured across different Echelle orders. In this paper, we present our stability analysis methodology and results for the Kavalur spectrograph. We also identify possible sources of error and discuss our strategy to mitigate them.
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Submitted 28 June, 2017;
originally announced June 2017.