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

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 $h\to0$, 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.