An Exponential Compact Higher Order Scheme

Abstract

An exponential compact higher order scheme is developed for stationary convection‐diffusion type of differential equations which inludes incompressible flow equations in stream function vorticity formulation. The scheme is, ingeneral, fourth order accurate however for one‐dimensional constant convection and diffusion coefficients, the scheme is O(h6) and produces a tri‐diagonal system of equations that can be solved efficiently using Thomas algorithm. For two‐dimensional problems, the scheme produces an O(h4+k4) accuracy over a compact nine point stencil which can be solved using any line iterative approach with alternate direction implicit (ADI) procedure. The efficiency of the developed scheme is measured using wave number analysis. The analysis shows that the developed scheme has a much better spectral resolution than any of the existing higher order schemes.