Nonlinear multigrid for fully-implicit and high-order accurate simluation of multiphase flow in porous media
High-order accurate and fully implicit finite difference schemes are widely used for multiphase flow problems. In this paper we analyze the use of point Gauss-Seidel relaxation in a nonlinear multigrid method for the resulting nonlinear systems of equations. Point Gauss-Seidel is unstable for calculating the steady-state of high-order accurate discretizations of the 2D convection equation. Here we present a local Fourier mode smoothing analysis for the transient case. It appears that point Gauss-Seidel is a good smoother provided that the time step is taken small enough. Numerical computations show good multigrid convergence rates for typical test problems.
|Finite difference methods (msc 65M06), Multigrid methods; domain decomposition (msc 65M55), Flows in porous media; filtration; seepage (msc 76S05)|
Molenaar, J. (1997). Nonlinear multigrid for fully-implicit and high-order accurate simluation of multiphase flow in porous media. CWI.