Nonlinear Multigrid for Fully-Implicit and High-Order Accurate Simulation of211 Multiphase Flow in Porous Media. Modelling, Analysis and Simulation

摘要

In this paper, we analyze the use of point Gauss-Seidel relaxation in a nonlinear211u001emultigrid method for the resulting nonlinear systems of equations. Point Gauss-211u001eSeidel is instable for calculating the steady-state of high-order accurate 211u001ediscretizations of the 2D convection equation. We present a local Fourier mode 211u001esmoothing analysis for the transient case. It appears that point Gauss-Seidel is 211u001ea good smoother provided that the time step taken is small enough. Numerical 211u001ecomputations show good multigrid convergence rates for typical test problems.