A New Compact Scheme in Exponential Form for Two-Dimensional Time-Dependent Burgers' and Navier-Stokes Equations

Abstract

A new compact implicit exponential scheme for Burgers' and Navier-Stokes equation is developed. The method has fourth order accuracy in space and second order accuracy in time. It uses only two time levels for computation and requires nine grid points at each time level. The stability of the method is proven for linearised Burgers' equation. It is applied to a modified Taylor vortex problem. Numerical examples confirm the theoretical results and show the accuracy of the method.