Large Scale Lattice Boltzmann Simulation for the Coupling of Free and Porous Media Flow
In this work, we investigate the interaction of free and porous media flow by large scale lattice Boltzmann simulations. We study the transport phenomena at the porous interface on multiple scales, i.e., we consider both, computationally generated pore-sc
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tract. In this work, we investigate the interaction of free and porous media flow by large scale lattice Boltzmann simulations. We study the transport phenomena at the porous interface on multiple scales, i.e., we consider both, computationally generated pore-scale geometries and homogenized models at a macroscopic scale. The pore-scale results are compared to those obtained by using different transmission models. Twodomain approaches with sharp interface conditions, e.g., of Beavers– Joseph–Saffman type, as well as a single-domain approach with a porosity depending viscosity are taken into account. For the pore-scale simulations, we use a highly scalable scheme with a robust second order boundary handling. We comment on computational aspects of the porescale simulation and on how to generate pore-scale geometries. The twodomain approaches depend sensitively on the choice of the exact position of the interface, whereas a well-designed single-domain approach can lead to a significantly better recovery of the averaged pore-scale results. Keywords: Lattice Boltzmann method · Pore-scale simulation · Two domain approach · Darcy Navier-Stokes coupling · Interface conditions
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Introduction
Transport phenomena in porous materials are important in many scientific and engineering applications such as catalysis, hydrology, tissue engineering and enhanced oil recovery. In the past several decades, flow in porous media has been studied extensively both experimentally and theoretically. We refer the interested reader to the textbook [1] and the references therein. In porous media flow, we usually distinguish between three scales: the pore-scale, the representative elementary volume (REV) scale and the domain scale. The REV is defined as the minimal element for which macroscopic characteristics of a porous flow can be observed. Because experimental setups for many practical questions may be too expensive or even impossible to realize, numerical simulation of porous media flow can be a useful complementary method to conventional experiments. To describe the flow in the bulk of the porous medium, Darcy’s law is commonly used in the form (1) μK−1 u = F − ∇p, c Springer International Publishing Switzerland 2016 T. Kozubek et al. (Eds.): HPCSE 2015, LNCS 9611, pp. 1–18, 2016. DOI: 10.1007/978-3-319-40361-8 1
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E. Fattahi et al.
where μ is the dynamic viscosity of the fluid, K is the permeability tensor of the porous medium, F is the body force, and u and p are averaged velocity and pressure quantities, respectively. However, when a porous medium and a free flow domain co-exist, e.g., in a river bed, there is no uniquely accepted model for the transition between the Darcy model and the free flow. Different approaches based on two-domain or on single-domain models are available. Using a singledomain in combination with the Brinkman equation that modifies Darcy’s law by a viscous term − μeff ∇2 u + μK−1 u = F − ∇p,
(Br)
allows to model a smooth transition (see e.g. [2–4]). Here μeff is an effective dynamic viscosity in the porous region. However,
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