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thornado+Flash-X: A Hybrid DG-IMEX and Finite-Volume Framework for Neutrino-Radiation Hydrodynamics in Core-Collapse Supernovae
Authors:
Eirik Endeve,
Vassilios Mewes,
J. Austin Harris,
M. Paul Laiu,
Ran Chu,
Steven A. Fromm,
Anthony Mezzacappa,
O. E. Bronson Messer,
W. Raphael Hix,
Stephen W. Bruenn,
Eric J. Lentz,
Klaus Weide,
Christian Y. Cardall,
Ann S. Almgren,
Anshu Dubey,
Sean M. Couch,
Philipp Moesta,
Donald E. Willcox
Abstract:
We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement (AMR)-based multiphysics simulation framework Flash-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment for…
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We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement (AMR)-based multiphysics simulation framework Flash-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $O(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino-matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino-electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved with a hybrid DG-FV representation of the fluid variables and operator-split evolution in Flash-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within Flash-X. thornado's neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.
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Submitted 2 January, 2026;
originally announced January 2026.
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Pixel-Resolved Long-Context Learning for Turbulence at Exascale: Resolving Small-scale Eddies Toward the Viscous Limit
Authors:
Junqi Yin,
Mijanur Palash,
M. Paul Laiu,
Muralikrishnan Gopalakrishnan Meena,
John Gounley,
Stephen M. de Bruyn Kops,
Feiyi Wang,
Ramanan Sankaran,
Pei Zhang
Abstract:
Turbulence plays a crucial role in multiphysics applications, including aerodynamics, fusion, and combustion. Accurately capturing turbulence's multiscale characteristics is essential for reliable predictions of multiphysics interactions, but remains a grand challenge even for exascale supercomputers and advanced deep learning models. The extreme-resolution data required to represent turbulence, r…
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Turbulence plays a crucial role in multiphysics applications, including aerodynamics, fusion, and combustion. Accurately capturing turbulence's multiscale characteristics is essential for reliable predictions of multiphysics interactions, but remains a grand challenge even for exascale supercomputers and advanced deep learning models. The extreme-resolution data required to represent turbulence, ranging from billions to trillions of grid points, pose prohibitive computational costs for models based on architectures like vision transformers. To address this challenge, we introduce a multiscale hierarchical Turbulence Transformer that reduces sequence length from billions to a few millions and a novel RingX sequence parallelism approach that enables scalable long-context learning. We perform scaling and science runs on the Frontier supercomputer. Our approach demonstrates excellent performance up to 1.1 EFLOPS on 32,768 AMD GPUs, with a scaling efficiency of 94%. To our knowledge, this is the first AI model for turbulence that can capture small-scale eddies down to the dissipative range.
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Submitted 22 July, 2025;
originally announced July 2025.
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Realizability-Preserving Discontinuous Galerkin Method for Spectral Two-Moment Radiation Transport in Special Relativity
Authors:
Joseph Hunter,
Eirik Endeve,
M. Paul Laiu,
Yulong Xing
Abstract:
We present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we so…
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We present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we solve for the Eulerian-frame energy and momentum. The proposed numerical method is designed to preserve moment realizability, which corresponds to moments defined by a nonnegative phase-space density. The realizability-preserving method is achieved with the following key components: (i) a discontinuous Galerkin (DG) phase-space discretization with specially constructed numerical fluxes in the spatial and energy dimensions; (ii) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (iii) a realizability-preserving conserved to primitive moment solver; (iv) a realizability-preserving implicit collision solver; and (v) a realizability-enforcing limiter. Component (iii) is necessitated by the closure procedure, which closes higher order moments nonlinearly in terms of primitive moments. The nonlinear conserved to primitive and the implicit collision solves are formulated as fixed-point problems, which are solved with custom iterative solvers designed to preserve the realizability of each iterate. With a series of numerical tests, we demonstrate the accuracy and robustness of this DG-IMEX method.
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Submitted 10 January, 2025;
originally announced January 2025.
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Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations
Authors:
William A. Porteous,
M. Paul Laiu,
Cory D. Hauck
Abstract:
We present a data-driven approach to construct entropy-based closures for the moment system from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the space-time discretization of the moment system and specific problem configurations such as initial and boundary conditions. Wi…
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We present a data-driven approach to construct entropy-based closures for the moment system from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the space-time discretization of the moment system and specific problem configurations such as initial and boundary conditions. With convex and $C^2$ approximations, this data-driven closure inherits several structural properties from entropy-based closures, such as entropy dissipation, hyperbolicity, and H-Theorem. We construct convex approximations to the Maxwell-Boltzmann entropy using convex splines and neural networks, test them on the plane source benchmark problem for linear transport in slab geometry, and compare the results to the standard, optimization-based M$_N$ closures. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than the M$_N$ closures.
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Submitted 16 June, 2021;
originally announced June 2021.
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A fast implicit solver for semiconductor models in one space dimension
Authors:
M. Paul Laiu,
Zheng Chen,
Cory D. Hauck
Abstract:
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved wi…
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Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.
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Submitted 9 July, 2019; v1 submitted 10 June, 2019;
originally announced June 2019.