Cross-validation of meshless Navier-Stokes solvers in porous media flows

TL;DR

This paper compares two meshless CFD solvers for pore-scale flow in porous media, validating their accuracy against literature data and exploring their performance across a wider porosity range.

Contribution

It introduces a consistent meshless discretization approach for both solvers and extends the analysis to porosities beyond existing studies.

Findings

Both solvers show excellent agreement with literature data.

The extended porosity analysis reveals new flow behavior insights.

Convergence and timing analyses support solver robustness.

Abstract

In this paper, two mesh-free CFD solvers for pore-scale fluid flow through porous media are considered, namely the Lattice Boltzmann Method with the two relaxation time collision term and the direct Navier-Stokes solver under the artificial compressibility limit. The porous media is built with a regular arrangement of spherical grains with variable radii, which allows control of the porosity. Both solvers use the same $h$-refined meshless spatial discretization to adequately capture the underlying geometry and the same Radial Basis Function (RBF) method to approximate the involved fields and partial differential operators. First, the results are compared with the data from the literature in terms of drag coefficient and permeability at different porosities achieving excellent agreement with the reported results. Next, the simulations are extended beyond the porosity range reported in the literature using proposed $h$-refined CFD solvers. The results are supported by convergence and timing analyses and discussions on meshless parameters such as stencil size and refinement settings.