New compact difference schemes on non-uniform collocated and staggered grids for convection-dominated flows

This paper deals with the formulation of the tridiagonal compact difference schemes for derivatives up to second-order with boundary stencils on non-uniform grids. A compact scheme for the first derivative with interpolation is also devised on staggered non-uniform grids. The developed schemes with non-uniform spacing transform to respective classical compact schemes for the case of uniform mesh spacing. The resolution, numerical diffusion, and anti-diffusion features of the devised schemes are evaluated using global spectral analysis. Applications to the direct numerical simulation (DNS) of two-dimensional lid-driven cavity (LDC) flow governed by Navier-Stokes equations and wave-propagation following linear rotating shallow water (LRSWE) equations with variable grid-spacing are discussed at different choices of parameters. Computed results are also compared with solutions available in the literature.