Developing an Efficient Multigrid Strategy for Solving Incompressible Flow

In this work, a multigrid acceleration technique is suitably developed for solving the two-dimensional incompressible Navier-Stokes equations using an implicit finite element volume method. In this regard, the solution domain is broken into a huge number of quadrilateral finite elements. The accurate numerical solution of a flow field can be achieved if very fine grid resolutions are utilized. Unfortunately, the standard implicit solvers need more computational time to solve larger size of algebraic set of equations which normally arise if fine grid distributions are used. Past experience has shown that the convergence of classical relaxation schemes perform an initial rapid decrease of residuals followed by a slower rate of decrease. This point indicates that a relaxation procedure is efficient for eliminating only the high frequency components of the residuals. This problem can be overcome using multigrid method, i.e., carrying out the relaxation procedure on a series of different grid sizes. There are different prolongation operators to establish a multigrid procedure. A new prolongation expression is suitably developed in this work. It needs constructing data during refining and coarsening stages which is fulfilled using suitable finite element interpolators. The extended formulations are finally used to test several different problems with available benchmark solutions. The results indicate that the current multigrid strategy effectively improves the bandit solver performance.