@Article{NMTMA-1-92, author = {}, 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} }