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Volume 1, Issue 1
A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids

Ruo Li, Xin Wang & Weibo Zhao

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

Published online: 2008-01

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  • Abstract

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.

  • Keywords

Multigrid, block LU-SGS, Euler equations, aerodynamics, airfoil.

  • AMS Subject Headings

65N22, 65N50, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-1-92, author = {Ruo Li, Xin Wang and Weibo Zhao}, title = {A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2008}, volume = {1}, number = {1}, pages = {92--112}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/10112.html} }
TY - JOUR T1 - A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids AU - Ruo Li, Xin Wang & Weibo Zhao JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 92 EP - 112 PY - 2008 DA - 2008/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/10112.html KW - Multigrid, block LU-SGS, Euler equations, aerodynamics, airfoil. AB -

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.

Ruo Li, Xin Wang and Weibo Zhao. (2008). A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids. Numerical Mathematics: Theory, Methods and Applications. 1 (1). 92-112. doi:
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