Efficient calculation of fluid transport in porous media with moving boundaries

A novel hybrid model combining the lattice Boltzmann (LB) and finite difference (FD) methods is proposed to simulate transport in through a junction of actively contracting lymphatic vessels, while also handling flow of interstitial liquid in the surrounding porous tissue. Details of the dynamically flexing walls and valves in the lymphatic vessel and its near vicinity are modeled using a high-resolution LB method, whereas overall efficiency was significantly improved by using low-resolution FD in the larger tissue domain distant from the vessel. Pressure and velocity conditions at the interface between subdomains of the two numerical methods are matched by imposing a partial bounce-back ratio in LB corresponding to the permeability coefficient $\kappa$ in Darcy's law for flow through porous media. Parameters governing the match between the algorithms at their interface can be estimated from the Kozeny-Carman relationship for porous media and further refined with a simpler, parallel flow geometry that also serves to validate the method. Test calculations show that the hybrid method is roughly four times faster than the LB method and permits computation over significantly larger domains. This method should be applicable to a large range of problems involving fluid flow in porous media with embedded conduits that have non-stationary boundaries.