TY - JOUR
T1 - A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids
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 - <p style="text-align: justify;">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.</p>