Evaluation of oscillation-free fluid-porous interface treatments for segregated finite volume flow solvers

Abstract

The volume-averaged approach to simulate flow in porous media is often used because of its practicality and computational efficiency. Derivation of the volume-averaged porous flow equations introduces additional porous resistance terms to the momentum equation. These porous resistance terms create body force discontinuities at fluid-porous interfaces, which may lead to spurious oscillations if not accounted for properly. A variety of techniques has been proposed to treat this problem, but only recently two approaches were developed by Nordlund et al. [Improved PISO algorithms for modeling density varying flow in conjugate fluid-porous domains. Journal of Computational Physics 2016;306:199–215. http://www.sciencedirect.com/science/article/pii/S0021999115007755. http://dx.doi.org/10.1016/j.jcp.2015.11.035; . Modified Rhie–Chow/PISO algorithm for collocated variable finite porous media flow solvers. No. 40 in ECI Symposium Series; 5th International Conference on Porous Media and Their Applications in Science, Engineering and Industry; 2014], concentrating on the combination of collocated grids and segregated solvers, which are commonly used for industrial applications. In this paper, we compared these two methods for the treatment of fluid-porous interfaces: (i) the Re-Distributed Resistivity (RDR) and (ii) the Face Consistent Pressure (FCP) methods, for a wide range of process conditions and porous media parameters, covering most practical porous media flow applications. The numerical robustness and accuracy of both methods were evaluated by applying a systematic quantitative comparison procedure. Both the RDR and the FCP approaches proved to be suitable for treating discontinuities in the porous resistance terms, yielding smooth solutions around the interface and good convergence with grid refinement. The RDR method was found to be the most robust method, particularly at very low Darcy numbers and on unstructured grids, distinguishing it from the FCP approach.