Chebyshev pseudospectral multi-domain technique for viscous flow calculation

Abstract

A novel Chebyshev pseudospectral multi-domain technique is introduced for the numerical solution of the Navier-Stokes equations in the primitive variable formulation. Careful consideration is given to the proper interface condition in the multi-domain method, which decomposes the solution domain into subdomains by overlapping one grid point. A finite difference approximation is used for the time discretization which transforms the system to a set of coupled equations which is then solved by an efficient computational boundary (CB) method. In the CB method, the pressure (Neumann) boundary conditions are simply obtained by re-arranging the discrete algebraic equations resulting from Chebyshev pseudospectral multi-domain approximation for the space variables. To demonstrate the effectiveness of this technique, we present some accurate computational results for calculating the driven cavity flows with Re up to 10 000 and for the flow past a circular cylinder with Re up to 100. The results for both applications are in good agreement with those of previous researchers.