High order asymptotic preserving discontinuous Galerkin methods for gray radiative transfer equations

11/28/2020
by   Tao Xiong, et al.
0

In this paper, we will develop a class of high order asymptotic preserving (AP) discontinuous Galerkin (DG) methods for nonlinear time-dependent gray radiative transfer equations (GRTEs). Inspired by the work <cit.>, in which stability enhanced high order AP DG methods are proposed for linear transport equations, we propose to pernalize the nonlinear GRTEs under the micro-macro decomposition framework by adding a weighted linear diffusive term. In the diffusive limit, a hyperbolic, namely Δ t=𝒪(h) where Δ t and h are the time step and mesh size respectively, instead of parabolic Δ t=𝒪(h^2) time step restriction is obtained, which is also free from the photon mean free path. The main new ingredient is that we further employ a Picard iteration with a predictor-corrector procedure, to decouple the resulting global nonlinear system to a linear system with local nonlinear algebraic equations from an outer iterative loop. Our scheme is shown to be asymptotic preserving and asymptotically accurate. Numerical tests for one and two spatial dimensional problems are performed to demonstrate that our scheme is of high order, effective and efficient.

READ FULL TEXT
research
11/30/2022

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers

In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP...
research
09/09/2021

An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations

In this paper, we develop an oscillation free local discontinuous Galerk...
research
07/19/2023

A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system

For time-dependent PDEs, the numerical schemes can be rendered bound-pre...
research
11/05/2021

Bounds-Preserving Lax-Wendroff Discontinuous Galerkin Schemes for Quadrature-Based Moment-Closure Approximations of Kinetic Models

The quadrature-based method of moments (QMOM) offers a promising class o...
research
07/18/2022

Is the Classic Convex Decomposition Optimal for Bound-Preserving Schemes in Multiple Dimensions?

Since proposed in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229: 3091–3...
research
02/27/2020

Structure aware Runge-Kutta time stepping for spacetime tents

We introduce a new class of Runge-Kutta type methods suitable for time s...
research
12/11/2022

A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations

We propose a model-data asymptotic-preserving neural network(MD-APNN) me...

Please sign up or login with your details

Forgot password? Click here to reset