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Implicit-explicit Runge-Kutta for radiation hydrodynamics I: Gray diffusion

Journal Article · · Journal of Computational Physics
 [1];  [1];  [1];  [1]
  1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
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Radiation hydrodynamics are a challenging multiscale and multiphysics set of equations. To capture the relevant physics of interest, one typically must time step on the hydrodynamics timescale, making explicit integration the obvious choice. On the other hand, the coupled radiation equations have a scaling such that implicit integration is effectively necessary in non-relativistic regimes. A first-order Lie-Trotter-like operator split is the most common time integration scheme used in practice, alternating between an explicit hydrodynamics step and an implicit radiation solve and energy deposition step. However, such a scheme is limited to first-order accuracy, and nonlinear coupling between the radiation and hydrodynamics equations makes a more general additive partitioning of the equations non-trivial. Here, we develop a new formulation and partitioning of radiation hydrodynamics with gray diffusion that allows us to apply (linearly) implicit-explicit Runge-Kutta time integration schemes. In conclusion, we prove conservation of total energy in the new framework, and demonstrate 2nd-order convergence in time on multiple radiative shock problems, achieving error 3–5 orders of magnitude smaller than the first-order Lie-Trotter operator split at the hydrodynamic CFL, even when Lie-Trotter applies a 3rd-order TVD Runge-Kutta scheme to the hydrodynamics equations.
Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
89233218CNA000001
OSTI ID:
2478088
Report Number(s):
LA-UR--23-24702
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 518; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (30)

An Analysis of Operator Splitting Techniques in the Stiff Case journal June 2000
Order conditions for numerical methods for partitioned ordinary differential equations journal December 1981
Radiative shock solutions with grey nonequilibrium diffusion journal May 2008
On linearly implicit IMEX Runge-Kutta methods for degenerate convection-diffusion problems modeling polydisperse sedimentation journal March 2016
Implicit–Explicit Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation journal October 2005
High Order Semi-implicit Schemes for Time Dependent Partial Differential Equations journal January 2016
Implicit and Implicit–Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order journal September 2017
All Mach Number Second Order Semi-implicit Scheme for the Euler Equations of Gas Dynamics journal May 2018
High-Order Semi-implicit Schemes for Evolutionary Partial Differential Equations with Higher Order Derivatives journal May 2023
Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics journal November 2021
Additive Runge–Kutta schemes for convection–diffusion–reaction equations journal January 2003
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations journal November 1997
Adaptive time-stepping and computational stability journal January 2006
A second order self-consistent IMEX method for radiation hydrodynamics journal November 2010
Second-order discretization in space and time for radiation-hydrodynamics journal June 2017
Linearly implicit all Mach number shock capturing schemes for the Euler equations journal September 2019
A unified formulation of splitting-based implicit time integration schemes journal January 2022
The development of a high-resolution Eulerian radiation-hydrodynamics simulation capability for laser-driven Hohlraums journal August 2022
Additive methods for the numerical solution of ordinary differential equations journal January 1980
Additive Runge-Kutta methods for stiff ordinary differential equations journal January 1983
On the Construction and Comparison of Difference Schemes journal September 1968
A Partially Implicit Method for Large Stiff Systems of ODEs with Only Few Equations Introducing Small Time-Constants journal October 1976
Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA) journal January 2013
A Generalized-Structure Approach to Additive Runge--Kutta Methods journal January 2015
Linearly Implicit IMEX Runge--Kutta Methods for a Class of Degenerate Convection-Diffusion Problems journal January 2015
Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections journal November 2019
A Two-moment Radiation Hydrodynamics Scheme Applicable to Simulations of Planet Formation in Circumstellar Disks journal January 2021
An Improved Method for Coupling Hydrodynamics with Astrophysical Reaction Networks journal August 2022
A Radiative Transfer Module for Relativistic Magnetohydrodynamics in the PLUTO Code journal June 2019
Split Runge-Kutta method for simultaneous equations journal July 1960

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Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS