A STUDY OF SEQUENTIAL SOLUTIONS FOR THE REDUCED COMPLETE NAVIER-STOKES EQUATIONS WITH MULTIGRID ACCELERATION

An efficient numerical method for the prediction of internal flow within ducts of arbitrary geometry is described. The Navier-Stokes and continuity equations are expressed in general nonorthogonal coordinates and are solved sequentially. All linear algebraic equations in the algorithm are solved by the Thomas algorithm. The method derives its efficiency mainly from the combination of a marching scheme along the main flow direction and the multigrid technique. For parabolic and slightly elliptic flows with recirculation, the marching-type algorithm can be used to solve the reduced or complete Navier-Stokes equations and produce comparable predictions. Comparisons are made between solutions from the complete/reduced Navier-Stokes equations and the effect of the equations on the algorithm's convergence rate is discussed. For flows with large recirculation, the reduced Navier-Stokes equations still produce a comparable solution to that of the complete Navier-Stokes equations, and the former equations are not only economical to compute but can also offer faster convergence. Both linear/nonlinear versions of the multigrid technique are incorporated in the marching-type algorithm. The overall acceleration of the convergence rate by the multigrid techique is shown by the computational results presented in this paper. More than three total mesh levels are recommended if the linear multigrid technique is used. Both linear/nonlinear versions of the multigrid technique are found to have a similar acceleration effect. The sequence in which the Navier-Stokes equations are solved is found to have influence on the convergence behaviour and the final residual level.