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

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.