Monolithic kinetic algorithm for heterogeneous porous media systems using a continuous one-domain approach

Abstract

We propose a lattice Boltzmann model (LBM) on standard lattices for simulating multi-dimensional, weakly compressible, isothermal flows within and around isotropic heterogeneous porous media. The model incorporates Darcy-Forchheimer drag and a Brinkman-like effective viscous stress tensor. In the hydrodynamic limit, it recovers a generalized volume-averaged formulation valid in both free-fluid and porous-medium regions. By relying on a single kinetic equation and a monolithic LBM algorithm, the formulation provides a one-domain solver for free-fluid/porous-medium interactions. Unlike previous LBM formulations for porous media, the proposed model recovers the correct porosity scaling of both the pressure and convective terms, while preserving the isotropy, and hence the Galilean invariance, of the viscous stress tensor. Linear and nonlinear drag, variable-porosity corrections, and additional body forces are incorporated through a consistent generalized forcing scheme. The model allows the speed of sound to be specified independently thereby improving computational efficiency. In addition, it includes a freely tunable effective bulk viscosity that can be used to enhance numerical stability. Model performance was evaluated using 2D benchmark flow problems. The ability of the proposed LBM model to simulate transport between free-fluid and heterogeneous porous regions within a one-domain framework enables a broad range of applications, particularly in early-stage, device-scale design studies of engineered porous structures with spatially varying porosity.