Acceleration and Stabilization of Algebraic Multigrid Solver Applied to Incompressible Flow Problems

摘要

Acceleration and stabilization of the Algebraic Multigrid solver (AMG) through n-th order Recursive Projection Method (RPM(n)) is described. It is shown that significant acceleration can be obtained if RPM(n) is applied to AMG during the inner iteration loop in a typical implicit incompressible CFD codes. In addition to accelerating the solution, RPM(n) provides increased stability to the AMG Solver extending it beyond its normal range of applicability in terms of matrix conditioning and M-matrix properties. RPM(n) algorithm allows the use of agglomerative AMG solver with simple smoothers to be effectively applied to matrices that are not an M-matrix. Theoretical foundations of RPM(n)-AMG algorithm are presented with some practical aspects of the algorithm implementation. Numerical experiments that involve pressure correction matrices of various sizes that appear in segregated pressure based algorithms together with coupled momentum and pressure matrices stemming from coupled pressure based algorithms are used to illustrate the effectiveness of the method.