An ILU Smoother for the Incompressible Navier-Stokes Equations in General Coordinates

ILU smoothers are good smoothers for linear multigrid methods. In this paper, a new ILU smoother for the incompressible Navier-Stokes equations, called CILU (Collective ILU), is designed, based on r-transformations. Existing ILU decompositions factorize the matrix with real elements. In CILU the elements of the matrix that is factorized are submatrices, corresponding to the set of physical variables. A multigrid algorithm using CILU as smoother is investigated. Average reduction factors and limiting reduction factors are measured to explore the performance of the algorithm. The results show that CILU is a good smoother.