High-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations

Abstract

An approach for the creation of high-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations is proposed. New versions of up to the eighth order of accuracy inclusive are implemented. For smooth solutions, numerical experiments on a sequence of grids show that the approximate solutions produced by these versions converge to the exact one with a high order of accuracy as h → 0, where h is the maximal linear cell size of a grid. The numerical results obtained for the benchmark problem of the lid-driven cavity flow suggest that the collocations and least squares method is well suited for the numerical simulation of viscous flows.