Derivation of New Staggered Compact Schemes with Application to Navier-Stokes Equations

Abstract

A method is proposed for the derivation of new classes of staggered compact derivative and interpolation operators. The algorithm has its roots in an implicit interpolation theory consistent with compact schemes and reduces to the computation of the required staggered derivatives and interpolated quantities as a combination of nodal values and collocated compact derivatives. The new approach is cost-effective, simplifies the imposition of boundary conditions, and has improved spectral resolution properties, on equal order of accuracy, with respect to classical schemes. The method is applied to incompressible Navier-Stokes equations through the implementation into a staggered flow solver with a fractional step procedure, and tested on classical benchmarks.