An Approach to the Implementation of the Multigrid Method with Full Approximation for CFD Problems

Abstract

This paper is devoted to the use of the multigrid method to accelerate calculations of compressible flows in a stationary formulation on unstructured grids. The multigrid method is used with the construction of a full approximation for each grid level (FAS MG—Full Approximation Scheme Multigrid). In the case of an unstructured grid, such a method can cause difficulties associated both with the construction of grid levels and transition operators between them, and with software implementation in the existing simulation code. The program needs to deal with several different discretizations at once. If the entire data structure, including arrays with grid data, topology, and time integration data, was designed to work on a single grid, then the implementation of the FAS MG can turn into a disaster involving rewriting the entire code. The purpose of this work is to achieve multiple acceleration of calculations at the cost of minimal effort. The problem of implementing the multigrid method on the basis of an existing software package that was not designed to work with several grid levels is solved. The implementation of the multigrid method in an MPI parallel code is carried out in such a way that there is no need to rewrite the program to work with multiple grids at all. Also, difficulties with constructing grid levels for an unstructured grid are avoided; agglomeration of cells is not used, and the number of faces per cell at coarse levels is not increased. In fact, this paper describes how to deploy a FAS MG accelerator in literally a week, even in code that is outdated from the point of view of software architecture.