Multidimensional upwind schemes for the solution of the incompressible Navier-Stokes equations

A residual distribution discretization of the incompressible Navier-Stokes equations is presented. It is first shown that residual distribution schemes for the advection equation can be written as Petrov-Galerkin finite element schemes on P1 finite elements. A residual distribution discretization of the incompressible Navier-Stokes equations is then developed, based on P1isoP2/P1 elements. The residual distribution Petrov-Galerkin weighting is applied to the momentum equations whereas Galerkin weighting is applied to the continuity equation. For the time discretization, a fractional step approach is adopted in which convection is treated in the first step, while the remaining Stokes problem is solved in the second step. The method is then applied to several 2D laminar test cases and compared with the method of characteristics/Galerkin approach used in the N3S finite element solver.