A conjugate-residual-FEM for incompressible viscous flow analysis (Q1094957)

The application of the conjugate residual method to the indefinite system resulting from the finite element approximation of the incompressible Navier-Stokes equations is studied. The possibility to use an element-by- element preconditioner for the acceleration of the convergence is also discussed. With this scheme, one can achieve significant savings in storage without ever forming the large total matrix. Furthermore, the hybrid finite element mesh, a mixture of the structured and unstructured mesh subdivisions, is employed to minimize the storage requirement. The numerical simulations of the Kármán vortex street, a driven cavity flow and the flow in a safety valve are presented to demonstrate the applicability of the proposed strategies.