2000 character limit reached
An asymptotic-preserving method for the three-temperature radiative transfer model (2402.19191v1)
Published 29 Feb 2024 in math.NA, cs.NA, math-ph, and math.MP
Abstract: We present an asymptotic-preserving (AP) numerical method for solving the three-temperature radiative transfer model, which holds significant importance in inertial confinement fusion. A carefully designedsplitting method is developed that can provide a general framework of extending AP schemes for the gray radiative transport equation to the more complex three-temperature radiative transfer model. The proposed scheme captures two important limiting models: the three-temperature radiation diffusion equation (3TRDE) when opacity approaches infinity and the two-temperature limit when the ion-electron coupling coefficient goes to infinity. We have rigorously demonstrated the AP property and energy conservation characteristics of the proposed scheme and its efficiency has been validated through a series of benchmark tests in the numerical part.
- Anderson acceleration and application to the three-temperature energy equations. Journal of Computational Physics, 347:1–19, 2017.
- Operator-based preconditioning for the 2-D 3-T energy equations in radiation hydrodynamics simulations. Journal of Computational Physics, 385:51–74, 2019.
- W. Bennett and R. McClarren. Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures. Proceedings of the Royal Society A, 477:20210119, 2021.
- A high order semi-implicit IMEX WENO scheme for the all-Mach isentropic Euler system. Journal of Computational Physics, 392:594–618, 2019.
- A colocalized scheme for three-temperature grey diffusion radiation hydrodynamics. Communications in Computational Physics, 31(04), 2022.
- Numerical resolution of a three temperature plasma model. Journal of Scientific Computing, 82(3):1–29, 2020.
- Numerical methods for coupling multigroup radiation with ion and electron temperatures. Communications in Applied Mathematics and Computational Science, 17:43–78, 2022.
- Methods for coupling radiation, ion, and electron energies in grey Implicit Monte Carlo. Journal of Computational Physics, 225(2):1695–1720, 2007.
- An implicit Monte Carlo scheme for calculating time and frequency dependent nonlinear radiation transport. Journal of Computational Physics, 8(3):313–342, 1971.
- An asymptotic-preserving IMEX method for nonlinear radiative transfer equation. Journal of Scientific Computing, 92:1–35, 2022.
- Solving nonlinear radiative transfer equation using IMEX PN method. Under Preparation, 2023.
- S. Ganesan and M. Singh. An operator-splitting finite element method for the numerical solution of radiative transfer equation. arXiv preprint arXiv:2122.07949, 2021.
- P.H. Hauschildt and E. Baron. A 3D radiative transfer framework I. Non-local operator splitting and continuum scattering problems. Astronomy & Astrophysics, 451:273–284, 2006.
- Some new discretization and adaptation and multigrid methods for 2-D 3-T diffusion equations. Journal of Computational Physics, 224:168–181, 2007.
- Implicit filtered PNsubscript𝑃𝑁P_{N}italic_P start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT for high-energy density thermal radiation transport using discontinuous galerkin finite elements. Journal of Computational Physics, 321:624–643, 2016.
- Computational methods of neutron transpot. American Nuclear Society, La Grange Park, Illinois, 1 1984.
- Weighted essentially non-oscillatory schemes. Journal of Computational Physics, 115:200–212, 1994.
- Semi-implicit time integration for PN thermal radiative transfer. Journal of Computational Physics, 227(16):7561–7586, 2008.
- On solutions to the Pn equations for thermal radiative transfer. Journal of Computational Phyiscs, 227:2864–2885, 2008.
- R. McClarren and J. Wöhlbier. Solutions for ion-electron-radiation coupling with radiation and electron diffusion. Journal of Quantitative Spectroscopy and Radiative Transfer, 112:1119–130, 2011.
- Parallel adaptive multigrid algorithm for 2-D 3-T diffusion equations. International Journal of Computer Mathematics, 81(3):361–374, 2004.
- A positivity-preserving finite volume scheme for three-temperature radiation diffusion equations. Applied Numerical Mathematics, 152:125–140, 2020.
- A continuous source tilting scheme for radiative transfer equations in implicit Monte Carlo. Journal of Computational and Theoretical Transport, 50(1), 2021.
- Y. Shi and H. Yong. A maximum-principle preserving implicit Monte Carlo method for a three-temperature radiative transfer model. Available at SSRN 4408635, 2023.
- The effects of electron thermal radiation on laser ablative shock waves from aluminum plasma into ambient air. Physics of Plasmas, 23:053107, 2016.
- C.D. Sijoy and S. Chaturvedi. TRHD: Three-temperature radiation-hydrodynamics code with an implicit non-equilibrium radiation transport using a cell-centered monotonic finite volume scheme on unstructured-grids. Computer Physics Communications, 190:98–119, 2015.
- C.D. Sijoy and S. Chaturvedi. Combining node-centered parallel radiation transport and higher-order multi-material cell-centered hydrodynamics methods in three-temperature radiation hydrodynamics code TRHD. Computer Physics Communications, 203:94–109, 2016.
- An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations. Journal of Computational Physics, 285(15):265–279, 2015.
- Accurate front capturing asymptotic preserving scheme for nonlinear gray radiative transfer equation. SIAM Journal on Scientific Computing, 43(3):B759–B783, 2021.
- M. Tang and X. Zhang. Semi-implicit front capturing schemes for the degenerate nonlinear radiative diffusion equation. Journal of Computational Physics, 436:110290, 2021.
- High order asymptotic preserving discontinuous Galerkin methods for gray radiative transfer equations. Journal of Computational Physics, 463:111308, 2022.
- A finite volume scheme preserving maximum principle for the system of radiation diffusion equations with three-temperature. SIAM Journal on Scientific Computing, 41(1):B93–B113, 2019.
- A fully asymptotic preserving decomposed multi-group method for the frequency-dependent radiative transfer equations. Journal of Computational Physics, 491:112368, 2023.