Co-located pressure-correction formulations on unstructured 2-D grids

Abstract

By extending a Navier±Stokes solution method for structured grids (SGs), a pressure-correction, ®nite-volume formulation for the numerical solution of laminar, incompressible, 2-D¯ows on unstructured grids (UGs) with triangular elements has been deviced. Since a co-located storage arrangement for all of the¯ow variables is used, the velocity and pressure ®elds should be arti®cially coupled. This is achieved through the careful extension of the Pressure-Weighted Interpolation Method (PWIM), successfully used for SGs in the past. In the ®rst part of the paper, the method formulation for UGs is analyzed. Then, the PWIM for UGs and the boundary conditions' implementation along solid walls are investigated, on the basis of two¯ow problems.

Development of unsteady algorithms for pressure-based unstructured solver for two-dimensional incompressible flows

“…This method works by adding a corrective term to the mass fluxes at the control volume faces, which is the basis of the pressure-weighted interpolation method (PWIM). Miller and Schmidt [29], Majumdar [30], Lambropoulos [31] also further extended the method to improve the approximation of the cell face velocity. Another remedy to the spurious pressure problem is to use a staggered mesh.…”