Numerical Solution of a Bifurcation Problem for the Boussinesq Equations at Low Prandtl Numbers by a Multigrid Method

摘要

A nonlinear multigrid method is used to solve a bifurcation problem in fluid mechanics. Time-derivatives are discretized by the Crank-Nicolson formula and spatial derivatives by the hybrid scheme. At each time step the equation system is solved by the multigrid algorithm. Bifurcation is observed only if the numerical solution at each time step is accurate enough. Sufficient accuracy is obtained by applying one defect correction iteration. The results are in agreement with those obtained by other authors using different methods. The computation cost is discussed. (Copyright (c) 1989 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)