Time stepping in discontinuous Galerkin method  

作　　者：LAI Wencong KHAN Abdul A 

机构地区：[1]Glenn Department of Civil Engineering, Clemson University, Clemson, S.C., USA

出　　处：《Journal of Hydrodynamics》2013年第3期321-329,共9页水动力学研究与进展B辑（英文版）

摘　　要：The time discretization in the Discontinuous Galerkin （DG） scheme has been traditionally based on the Total Variation Diminishing （TVD） second-order Runge-Kutta （RK2） scheme. Computational efficiency and accuracy with the Euler Forward （EF） and the TVD second-order RK2 time stepping schemes in the DG method are investigated in this work. Numerical tests are condu- cted with the scalar Burgers equation, 1-D and 2-D shallow water flow equations. The maximum Courant number or time step size required for stability for the EF scheme and RK2 scheme with different slope limiters are compared. Numerical results show that the slope limiters affect the stability requirement in the DG method. The RK2 scheme is generally more diffusive than the EF scheme, and the RK2 scheme allows larger time step sizes. The EF scheme is found to be more efficient and accurate than the RK2 scheme in the DG method in computation.The time discretization in the Discontinuous Galerkin （DG） scheme has been traditionally based on the Total Variation Diminishing （TVD） second-order Runge-Kutta （RK2） scheme. Computational efficiency and accuracy with the Euler Forward （EF） and the TVD second-order RK2 time stepping schemes in the DG method are investigated in this work. Numerical tests are condu- cted with the scalar Burgers equation, 1-D and 2-D shallow water flow equations. The maximum Courant number or time step size required for stability for the EF scheme and RK2 scheme with different slope limiters are compared. Numerical results show that the slope limiters affect the stability requirement in the DG method. The RK2 scheme is generally more diffusive than the EF scheme, and the RK2 scheme allows larger time step sizes. The EF scheme is found to be more efficient and accurate than the RK2 scheme in the DG method in computation.

关 键 词：Discontinuous Galerkin （DG） method Euler Forward （EF） scheme second-order Runge-Kutta scheme 

分 类 号：O241.82[理学—计算数学] TP18[理学—数学]