Multigrid technique and Optimized Schwarz method on block-structured grids with discontinuous interfaces

Abstract

An Optimized Schwarz method using Robin boundary conditions for relaxation scheme is presented in the frame of Multigrid method on discontinuous grids. At each iteration the relaxation scheme is performed in two steps: one step with Dirichlet and another step with Robin boundary conditions at inner block boundaries. A Robin parameter that depends on grid geometry and grid discontinuity at block interfaces is introduced. The general solution algorithm is based on SIMPLE method and a conservative finite-volume scheme on blockstructured grids with discontinuous interfaces. The multigrid method is used to obtain the solution of pressure-correction equation where an Incomplete Block LU factorization is used as the relaxation scheme. Solution on the coarsest grid is done with an Incomplete Block LU preconditioned Conjugate Gradient method. Results from computations of laminar flows around a circular cylinder on grids with nonmatching interfaces are presented.