An implicit finite element scheme using the concept of PISO method has been developed to solve the incompressible as well as compressible viscous flow problems in all speed range. In this study, a new pressure equation is proposed such that both the hyperbolic term related with the density variations and elliptic term reflecting the incompressibility constraint are included. The numerical solution converges relatively very fast when the problem is steady, since it dispenses with pressure-related underrelaxation parameter and allows large time step size. Further, the efficient iterative matrix solvers such as PCGS and ICCG have made the present method very powerful in simulating the three-dimensional flow problems. Using unstructured grid system having a matrix of large band size can also enjoy this benefit of the method.
The two-dimensional and three-dimensional driven cavity flow and the transient flow around a circular cylinder are computed to test the efficiency and accuracy of the scheme. In addition, the transient flow around two circular cylinders in transverse arrangement is simulated on an unstructured triangular grid formed by advancing front technique. In part of compressible flow formulation, interaction of the shock wave and boundary layer on a plate has been solved.
Finally, the three-dimensional vortical flow around a half-open tilting disc valve is simulated using the present finite element method. Computational result shows that flow is separated along the forward part of circular edge of the disc and reattached in the middle of the disc back face, forming a recirculating flow region. Vortex tubes are consequently generated in the wake of the disc the strength of which depends on the Reynolds number. It is shown that in the confined duct flow secondary vortex tubes are induced and there arises axial velocity overshoot in the symmetric midplane of the duct flow.
