Stability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scaling

DOI10.1016/j.jcp.2020.109485zbMath1440.65147OpenAlexW3023885746MaRDI QIDQ2194326

Zhichao Peng, Fengyan Li, Yingda Cheng, Jing-Mei Qiu

Publication date: 25 August 2020

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2020.109485

zbMATH Keywords

numerical stabilityhigh orderdiscontinuous Galerkinasymptotic preservinginitial layerkinetic transport equation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Transport equations (35Q49)

Related Items (11)

Hyperbolic balance laws: modeling, analysis, and numerics. Abstracts from the workshop held February 28 -- March 6, 2021 (hybrid meeting) ⋮ An asymptotic-preserving IMEX method for nonlinear radiative transfer equation ⋮ Solving multiscale steady radiative transfer equation using neural networks with uniform stability ⋮ High order asymptotic preserving discontinuous Galerkin methods for gray radiative transfer equations ⋮ Asymptotic Preserving and Uniformly Unconditionally Stable Finite Difference Schemes for Kinetic Transport Equations ⋮ A fully asymptotic preserving decomposed multi-group method for the frequency-dependent radiative transfer equations ⋮ High order positivity-preserving nodal discontinuous Galerkin methods for anisotropic diffusion problems ⋮ Uniform stability for local discontinuous Galerkin methods with implicit-explicit Runge-Kutta time discretizations for linear convection-diffusion equation ⋮ Spatial second-order positive and asymptotic preserving unified gas kinetic schemes for radiative transfer equations ⋮ Stability-enhanced AP IMEX1-LDG Method: Energy-based Stability and Rigorous AP Property ⋮ Asymptotic Preserving IMEX-DG-S Schemes for Linear Kinetic Transport Equations Based on Schur Complement

Cites Work

• Unnamed Item
• High order asymptotic preserving DG-IMEX schemes for discrete-velocity kinetic equations in a diffusive scaling
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes. II
• Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• High-Order Asymptotic-Preserving Methods for Fully Nonlinear Relaxation Problems
• Analysis of Asymptotic Preserving DG-IMEX Schemes for Linear Kinetic Transport Equations in a Diffusive Scaling
• A Robust Multigrid Preconditioner for $S_N$DG Approximation of Monochromatic, Isotropic Radiation Transport Problems
• Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit
• Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit
• Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Initial and boundary conditions for diffusive linear transport problems
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
• Uniform Stability of a Finite Difference Scheme for Transport Equations in Diffusive Regimes
• Micro-Macro Schemes for Kinetic Equations Including Boundary Layers
• Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit
• Flux-Explicit IMEX Runge--Kutta Schemes for Hyperbolic to Parabolic Relaxation Problems
• A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit

This page was built for publication: Stability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scaling