A coupled pressure based solver for simulating variable porosity flows on coarse grids

In this presentation two new formulations are presented for simulating variable porosity single-phase flows on collocated grids. These have been developed on a coupled pressure-based solver that uses the finite difference discretization method. The proposed formulations use the Rhie-Chow interpolation method for avoiding checkerboarding problems. Additionally, the novelties introduced here are discretization schemes for implicit and explicit source terms. The numerical treatment of high-valued source terms on collocated grids has been researched extensively. However, with large discontinuities in porosity, physical oscillations can appear in the solution. The explicit formulation developed here can simulate large discontinuities in porosity on coarsely collocated grids without unphysical oscillations. This is also the case for the implicit formulation which can simulate a wider range of permeabilities and flow speeds, again, without instabilities in the solution. The results of these methods are comparable to using a staggered grid. To demonstrate this new method, the numerical methods will be explained, and a series of test cases will be shown. These test cases will range from incompressible to high Mach number flows with large discontinuities in the porosity and permeability. While the current work uses a finite difference formulation on structured grids, it is proposed that this could be extended to more general finite volume codes.