Navier-Stokes solution by new compact schemes for incompressible flow

Abstract

This chapter discusses the development of Navier–Stokes equation for incompressible flows by a new compact scheme of the spectral resolution obtained by a spectral method. The optimized schemes are very high resolution methods, where particular attention is paid to avoid numerical instability introduced by currently used boundary closure techniques. A constrained optimization is performed in the chapter that maximizes spectral resolution. These new schemes are used to solve two fluid flow instability problems that are difficult to solve using explicit schemes. The effect of windshear past bluff-body and predicting a vortex-induced instability are the two problems involved. The compact schemes show tremendous speed up because of the use of much lesser number of grid points.