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

Summary 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.