Hybrid sixth order spatial discretization scheme for non-uniform Cartesian grids

Abstract

A class of high accuracy compact schemes used to solve wave problems and the Navier Stokes equation (NSE) on a non-uniform Cartesian grid is presented here. Global spectral analysis (GSA) performed with the help of model one-dimensional (1D) convection equation reveals that the scheme has excellent dispersion relation preserving properties and scale resolution. The developed analysis tool is used to provide resolution and numerical properties for grids with randomly varying spacing between the nodes, for the first time.The results of the benchmark problem of two-dimensional (2D) convection equation are used to validate with exact solution. Two-dimensional NSE is also solved for (i) square lid-driven cavity (LDC) at different Reynolds numbers and (ii) Taylor-Green vortex problem, as evidences of effectiveness and accuracy of the new scheme. These establish the robustness of the non-uniform high order compact scheme developed here for simulations of fluid flow and wave phenomena.