$$\mathbf {p}$$-Multigrid High-Order Discontinuous Galerkin Solution of Compressible

2021 ◽  
pp. 197-238
Author(s):  
A. Colombo ◽  
A. Ghidoni ◽  
G. Noventa ◽  
S. Rebay
Keyword(s):  
Discontinuous Galerkin ◽  
High Order ◽  
Galerkin Solution

HIGH-ORDER DISCONTINUOUS GALERKIN SOLUTION OF LOW-RE VISCOUS FLOWS

2009 ◽  
Vol 23 (03) ◽  
pp. 309-312
Author(s):  
HONGQIANG LU
Keyword(s):  
Discontinuous Galerkin ◽  
Euler Method ◽  
High Order ◽  
Navier Stokes ◽  
High Order Schemes ◽  
Seidel Method ◽  
Backward Euler ◽  
Dg Method ◽  
Galerkin Solution ◽  
Nonlinear Discrete System

In this paper, the BR2 high-order Discontinuous Galerkin (DG) method is used to discretize the 2D Navier-Stokes (N-S) equations. The nonlinear discrete system is solved using a Newton method. Both preconditioned GMRES methods and block Gauss-Seidel method can be used to solve the resulting sparse linear system at each nonlinear step in low-order cases. In order to save memory and accelerate the convergence in high-order cases, a linear p-multigrid is developed based on the Taylor basis instead of the GMRES method and the block Gauss-Seidel method. Numerical results indicate that highly accurate solutions can be obtained on very coarse grids when using high order schemes and the linear p-multigrid works well when the implicit backward Euler method is employed to improve the robustness.

An improvement of classical slope limiters for high-order discontinuous Galerkin method

2009 ◽  
Vol 59 (4) ◽  
pp. 423-442 ◽  
Author(s):  
R. Ghostine ◽  
G. Kesserwani ◽  
R. Mosé ◽  
J. Vazquez ◽  
A. Ghenaim
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
High Order ◽  
Slope Limiters
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