Paper Info
Title
Stability-Enhanced Ap Imex1-Ldg Method: Energy-Based Stability And Rigorous Ap Property
Abstract
In our recent work [Z. Peng et al., J. Comput. Phys., 415 (2020), 109485], a family of high-order asymptotic preserving (AP) methods, termed IMEX-LDG methods, are designed to solve some linear kinetic transport equations, including the one-group transport equation in slab geometry and the telegraph equation, in a diffusive scaling. As the Knudsen number epsilon goes to zero, the limiting schemes are implicit discretizations to the limiting diffusive equation. Both Fourier analysis and numerical experiments imply the methods are unconditionally stable in the diffusive regime when epsilon << 1. In this paper, we develop an energy approach to establish the numerical stability of the IMEX1-LDG method, the subfamily of the methods that is first-order accurate in time and arbitrary order in space, for the model with general material properties. Our analysis is the first to simultaneously confirm unconditional stability when epsilon << 1 and the uniform stability property with respect to epsilon. To capture the unconditional stability, we propose a novel discrete energy and explore various stabilization mechanisms of the method and their relative contributions in different regimes. A general form of the weight function, introduced to obtain the unconditional stability for epsilon << 1, is also for the first time considered in such stability analysis. Based on uniform stability, a rigorous asymptotic analysis is then carried out to show the AP property.
Year
DOI
Venue
2021
10.1137/20M1336503
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
DocType
Volume
kinetic transport equation, multiscale, asymptotic preserving, discontinuous Galerkin, numerical stability, energy approach
Journal
59
Issue
ISSN
Citations 
2
0036-1429
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Peng Zhichao100.68
Yingda Cheng220120.27
Qiu Jing-Mei300.34
Li Fengyan400.68