Chebyshev spectral and pseudospectral solutions of the Navier-Stokes equations

Abstract

This paper presents numerical solutions obtained by Chebyshev approximations of thermal convection flows. In the first part, a Chebyshev Tau method with influence matrix technique for the pressure computation is applied to the simulation of convective phenomena in liquid metals. Some results are compared with those produced by finite elements. In the second part, a pseudospectral algorithm using finite element preconditioning for the momentum equations and finite difference preconditioning for the temperature equation treats thermal convection in a fluid whose viscosity is strongly temperature dependent. As finite element-pseudospectral schemes (FE-PS) are recent, some test problems are solved to assess their performance.