Simulation of micro-scale porous flow using Smoothed Particle Hydrodynamics

Abstract

Fluid flow in a porous medium is a well-studied aspect of applied mathematics with significant real-world application. The standard modelling approach for this type of flow is to homogenise the porous structure. A dual-scale model, with the smaller scale at the pore-scale, would possibly capture the fluid mechanical phenomena more faithfully than a volume averaged approach. We investigate the significance of the microstructure shape on the flux through the medium. We also evaluate whether smoothed particle hydrodynamics may be viable in a dual-scale model. We find that varying the shape of the porous structure causes the average flux to vary significantly. This contradicts the assumption commonly made that only the porosity is important. We conclude that there is significant information present in the dualscale model that is lost by a volume averaged model. We also find that

Couple Microscale Periodic Patches to Simulate Macroscale Emergent Dynamics

“…Alternative multiscale methods that have been proposed are based upon analogous simulations at the microscale level. For example, in the flow through a porous medium, Hassard et al [18] used smoothed particle hydrodynamics on the microscale to estimate macroscale volume averaged fluxes, with a view to forming a two-scale model that appears like a finite-volume scheme on the macroscale. For general gradient-driven transport processes, Carr et al [10] correspondingly proposed an extended distributed microstructure model where the macroscale flux is determined as the average of microscale fluxes within microcells.…”

Couple microscale periodic patches to simulate macroscale emergent dynamics

“…Alternative multiscale methods that have been proposed are based upon analogous simulations at the microscale level. Foe example, in the flow through a porous medium, Hassard et al (2016) used smoothed particle hydrodynamics on the microscale to estimate macroscale volume averaged fluxes, with a view to forming a two-scale model that appears like a finite volume scheme on the macroscale. For general gradient driven transport processes, Carr, Perré, and Turner (2016) correspondingly proposed an Extended Distributed Microstructure Model where the macroscale flux is determined as the average of microscale fluxes within micro-cells.…”