A Multigrid Method for 2-D MGD Flow Control Analysis

In this paper, the authors de velop a multigrid FAS (Full Approximation Scheme) for accelerating convergence for solving the magnetoaerodynamic (MGD) flow electric field, which is described by a Poisson-type equation. The equation is discretized by a second order central difference and the residual is also discretized by a 2 nd order central difference. To deal with anisotropic effect for general coordinate with non-uniform grids, alternating direction implicit (ADI) method is applied as a smoother. It is shown that the multigrid efficie ncy is achieved for the 2 nd order scheme and it can be used in general coordinate s. In order to accommodate both linear and non -linear problems, the multigrid full approximation scheme (FAS) method is used. Test cases for 2 D Poisson equations and several verification problems are considered to explore the accuracy of the implementation and the efficiency of the multigrid method. The performance characteristics of the algorithm are discussed and illustrations are made.