Novel pressure inlet and outlet boundary conditions for Smoothed Particle Hydrodynamics, applied to real problems in porous media flow

Abstract

In this work, new pressure inlet and outlet boundary conditions are developed for Smoothed Particle Hydrodynamics (SPH) that allow the natural development of in- and out-flow velocity profiles for any complex and irregular domain shapes and flow paths. The use of numerical methods to evaluate the permeability of real porous media is well established in the literature and SPH is a method that would seem ideally suited to such modelling. Examples applying SPH to real porous media are, however, scarce. A key limitation arises due to challenges associated with implementing natural inlet and outlet conditions on a highly irregular flow domain (as with porous rocks, bone, bioengineered ceramics, etc.). The method developed here enables generalised constant pressure open boundaries to be specified. This functions by controlling incoming or outgoing particle velocity to assure a target pressure and density is achieved at the theoretical boundary interface. The velocity correction term is derived from the SPH continuity density expression. New variations of no-slip and mirror boundaries are also presented. The developed method is shown to be highly robust and is implemented within a corrected kernel form of SPH (CSPH) to evaluate accuracy. Simulations are presented for several test cases including flow through a 2D channel junction, and permeability evaluation of an ideal 3D porous media across a range of porosities, and for 4 samples of porous trabecular bone taken from microCT scans. Results demonstrate excellent agreement with existing benchmarks, and with comparative results produced using the commercial ANSYS Fluent software package. The consistency of the developed boundary conditions enables accurate solution of a wide range of complex flow problems using SPH that has not been possible before.