A semi-Lagrangian discontinuous Galerkin (DG) - local DG method for solving convection-diffusion equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:409

Article

Ding, Mingchang¹  Cai, Xiaofeng¹  Guo, Wei²  Qiu, Jing-Mei¹ 

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 70409 USA

关键词: Convection-diffusion equation;    Semi-Lagrangian;    Discontinuous Galerkin (DG) method;    Local DG method;    Implicit Runge-Kutta method;    Stability analysis;   

DOI  :  10.1016/j.jcp.2020.109295

来源: Elsevier

【 摘 要 】

In this paper, we propose an efficient high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for solving linear convection-diffusion equations. The method generalizes our previous work on developing the SLDG method for transport equations [5], making it capable of handling additional diffusion and source terms. Within the DG framework, the solution is evolved along the characteristics; while the diffusion term is discretized by the local DG (LDG) method and integrated along characteristics by implicit Runge-Kutta methods together with source terms. The proposed method is named the 'SLDG-LDG' method and enjoys many attractive features of the DG and SL methods. These include the uniformly high order accuracy (e.g. third order) in space and in time, compact, mass conservative, and stability under large time stepping size. An L-2 stability analysis is provided when the method is coupled with the first order backward Euler discretization. Effectiveness of the method are demonstrated by a group of numerical tests in one and two dimensions. (C) 2020 Elsevier Inc. All rights reserved.

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