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Coarse grid projection (CGP) methodology is a novel multigrid method forsystems involving decoupled nonlinear evolution equations and linear ellipticPoisson equations. The nonlinear equations are solved on a fine grid and thelinear equations are solved on a corresponding coarsened grid. Mappingoperators execute data transfer between the grids. The CGP framework isconstructed upon spatial and temporal discretization schemes. This frameworkhas been established for finite volume/difference discretizations as well asexplicit time integration methods. In this article we present for the firsttime a version of CGP for finite element discretizations, which uses asemi-implicit time integration scheme. The mapping functions correspond to thefinite-element shape functions. With the novel data structure introduced, themapping computational cost becomes insignificant. We apply CGP topressure-correction schemes used for the incompressible Navier-Stokes flowcomputations. This version is validated on standard test cases with realisticboundary conditions using unstructured triangular meshes. We also pioneerinvestigations of the effects of CGP on the accuracy of the pressure field. Itis found that although CGP reduces the pressure field accuracy, it preservesthe accuracy of the pressure gradient and thus the velocity field, whileachieving speedup factors ranging from approximately 2 to 30. Exploring theinfluence of boundary conditions on CGP, the minimum speedup occurs forvelocity Dirichlet boundary conditions, while the maximum speedup occurs foropen boundary conditions. We discuss the CGP method as a guide for partial meshrefinement of incompressible flow computations and show its application forsimulations of flow over a backward-facing step and flow past a cylinder.

A Finite-Element Coarse-Grid Projection Method: A Dual Acceleration/Mesh Refinement Tool for Incompressible Flows