TY - JOUR
T1 - A semi-Lagrangian discontinuous Galerkin (DG) – local DG method for solving convection-diffusion equations
AU - Ding, Mingchang
AU - Cai, Xiaofeng
AU - Guo, Wei
AU - Qiu, Jing Mei
N1 - Funding Information:
Research is supported by NSF grant NSF-DMS-1830838 (Program manager: Dr. Leland M. Jameson).Research of the first, second and last author is supported by NSF grant NSF-DMS-1522777 and NSF-DMS-1818924 (Program manager: Dr. Leland M. Jameson), Air Force Office of Scientific Research FA9550-18-1-0257 (Program manager: Dr. Fariba Fahroo).
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/5/15
Y1 - 2020/5/15
N2 - 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 L2 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.
AB - 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 L2 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.
KW - Convection-diffusion equation
KW - Discontinuous Galerkin (DG) method
KW - Implicit Runge-Kutta method
KW - Local DG method
KW - Semi-Lagrangian
KW - Stability analysis
UR - http://www.scopus.com/inward/record.url?scp=85079519194&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2020.109295
DO - 10.1016/j.jcp.2020.109295
M3 - Article
AN - SCOPUS:85079519194
VL - 409
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 109295
ER -