An Algebraic Multigrid Solver for Navier-Stokes Problems in the Discrete Second-Order Approximation

An algebraic multigrid scheme is presented for solving the discrete Navier-Stokes equations to second-order accuracy using the defect-correction method. Solutions have been obtained for problems involving both structured and unstructured meshes, with the resolution and resolution grading controlled by global and local mesh refinements. The solver is efficient and robust to the extent that no underrelaxation of variables has been required to ensure convergence, but rates of convergence can be improved with small amounts of underrelaxation of the velocity-pressure coupling. Provided that the computational mesh can resolve the flow field, convergence characteristics are almost mesh independent. Rates of convergence actually improve with refinement, asymptotically approaching mesh independent values. For extremely coarse meshes where dispersive truncation errors would be expected to prevent convergence (or even induce divergence), solutions can still be obtained by using explicit underrelaxation in the iterative cycle.