A Pressure-Weighted Upwind Scheme In Unstructured Finite-Element Grids

Today the finite element method is known as a powerful tool capable of solving complex flow in complex geometries. Additionally, the unstructured grid topology is a complementary tool which effectively increases computational efficiencies. On the other hand, the finite element volume methods incorporate the advantages of conserving the conservative quantities within elements. However, the accurate conservation statements need utilizing suitable approximation at cell faces. In convection dominated flows, upwind-based schemes are strongly utilized. However, these schemes do not suffice to incorporate the details of pressure field in the approximation. Therefore, the pressure-weighted upwind scheme is a better choice for a flow field with high pressure gradients. In this work, a pressure-weighted upwind scheme is suitably extended for solving incompressible flow on unstructured grids. Subsequently, a remedy is given for the problem associated with using equal-order pressure and velocity interpolations. Eventually, the extended formulations are validated against suitable benchmark problems involving small and large scale recirculation zones. Comparing with the benchmark solutions, the current results are excellent.

[1]  Peter Hansbo,et al.  A velocity pressure streamline diffusion finite element method for Navier-Stokes equations , 1990 .

[2]  Masoud Darbandi,et al.  Application of an all-speed flow algorithm to heat transfer problems , 1999 .

[3]  Layne T. Watson,et al.  Steady Viscous Flow in a Triangular Cavity , 1994 .

[4]  Jean-Luc Guermond,et al.  Calculation of Incompressible Viscous Flows by an Unconditionally Stable Projection FEM , 1997 .

[5]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: II. Beyond SUPG , 1986 .

[6]  Tayfun E. Tezduyar.  Finite element computation of unsteady incompressible flows involving moving boundaries and interfaces and iterative solution strategies , 1992 .

[7]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .

[8]  Peter Hansbo,et al.  A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equation , 1990 .

[9]  J. Donea.  A Taylor–Galerkin method for convective transport problems , 1983 .

[10]  C. Prakash,et al.  AN IMPROVED CONTROL VOLUME FINITE-ELEMENT METHOD IFOR HEAT AND MASS TRANSFER, AND FOR FLUID FLOW USING EQUAL-ORDER VELOCITY-PRESSURE INTERPOLATION , 1986 .

[11]  D. Mavriplis.  UNSTRUCTURED GRID TECHNIQUES , 1997 .

[12]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[13]  ShakibFarzin,et al.  A new finite element formulation for computational fluid dynamics , 1991 .