Numer. Math. Theor. Meth. Appl., 1 (2008), pp. 92-112.

A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids

Ruo Li 1*, Xin Wang 2, Weibo Zhao 1

1 LMAM & School of Mathematical Sciences, Peking University, Beijing, China.
2 LMAM, CCSE & School of Mathematical Sciences, Peking University, Beijing, China.

Received 21 January, 2007; Accepted (in revised version) 28 November, 2007


We propose an efficient and robust algorithm to solve the steady Euler equations on unstructured grids. The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel (LU-SGS) iteration as its smoother. To regularize the Jacobian matrix of Newton-iteration, we adopted a local residual dependent regularization as the replacement of the standard time-stepping relaxation technique based on the local CFL number. The proposed method can be extended to high order approximations and three spatial dimensions in a nature way. The solver was tested on a sequence of benchmark problems on both quasi-uniform and local adaptive meshes. The numerical results illustrated the efficiency and robustness of our algorithm.

AMS subject classifications: 65N22, 65N50, 65N55
Key words: Multigrid, block LU-SGS, Euler equations, aerodynamics, airfoil.

*Corresponding author.
Email: (R. Li), (X. Wang), (W. Zhao)

The Global Science Journal