Fourth order compact finite volume scheme on nonuniform grids with multi-blocking

Abstract

We have developed a fourth order compact finite volume method for the solution of low Mach number compressible flow equations on arbitrary nonuniform grids. The formulation presented here uses collocated grid that preserves fourth order accuracy on nonuniform meshes. This was achieved by introduction of a new fourth order method for calculation of cell and face averaged metrics. A special treatment of nonlinear terms is used to guarantee the stability of the fourth order compact method. Moreover an approach for applying this method to multi-block domains is presented for complicated geometries and parallel processing applications. Several test cases including the flow in a lid-driven cavity, laminar flow over a flat plate, decay of the Taylor vortex, and transient flow behind a backward facing step show the accuracy, efficiency, and stability of the method in single and multi-block domains. To the best of our knowledge, this is the first symmetric compact method in the finite volume form that can achieve full fourth order accuracy in solving fluid flow equations on nonuniform collocated grids without any stability problems.