Multigrid methods to accelerate convergence of element-by-element solution algorithms for viscous incompressible flows Original Research Article

The use of iterative solvers for large systems of equations results in a slow convergence rate after the small wave length error components are resolved. For a fixed convergence tolerance limit, the error resolution capability of an iterative solver is a function of the mesh density. Two iterative solvers (GMRES and ORTHOMIN), which utilize the element-by-element (EBE) data structure of the finite element mesh, are studied to demonstrate this behavior. A significant improvement in the accuracy of the solution and the rate of convergence is achieved for these iterative solvers by using a successive mesh refinement scheme (like in a multigrid method). This approach is found to better resolve both the large and the small scale flow phenomenon for a fine mesh while satisfying the convergence criterion in a fraction of the CPU time required by the standard iterative methods. An iterative penalty finite element model is used to solve the governing equations for laminar, incompressible, isothermal fluid flows. The solution accuracy and CPU time savings are demonstrated for two sample problems.