Coupling staggered-grid and MPFA finite volume methods for free flow/porous-medium flow problems

Abstract

A discretization is proposed for models coupling free flow with anisotropic porous medium flow.Our approach employs a staggered grid finite volume method for the Navier-Stokes equations in the free flow subdomain and a MPFA finite volume method to solve Darcy flow in the porous medium. After appropriate spatial refinement in the free flow domain, the degrees of freedom are conveniently located to allow for a natural coupling of the two discretization schemes. In turn, we automatically obtain a more accurate description of the flow field surrounding the porous medium.Numerical experiments highlight the stability and applicability of the scheme in the presence of anisotropy and show good agreement with existing methods, verifying our approach.

A Dynamic and Fully Implicit Non‐Isothermal, Two‐Phase, Two‐Component Pore‐Network Model Coupled to Single‐Phase Free Flow for the Pore‐Scale Description of Evaporation Processes

“…are constructed. We refer to (Schneider et al, 2020) for details on the discretized form of Equation 1. The primary variables of the free-flow model are p g , v g , T, and water g…”

DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

“…Figure 1 depicts the configurations of control volumes and sub-faces as chosen in DuMu x , exemplarily for the tpfa, mpfa and the box scheme. A corresponding illustration for the mac scheme can be found, for example, in [43]. As illustrated in Fig.…”

“…The presented multi-domain concept has been successfully used to implement models with coupled flow and transport processes in vascularized brain tissue [10,51], root-soil interaction models in the vadose zone [9], flow and transport models for fractured rock systems [15,52], coupled porous medium flow and atmosphere flow (Darcy-Navier-Stokes) at the soil surface [43], and a model that couples a pore-network model with a Navier-Stokes model [53].…”

“…A versatile implementation of cell-centered mpfa-o scheme is now usable with all models [15]. The Navier-Stokes models are redesigned to use a mac scheme on a staggered grid [56,43,53], including a Reynolds-averaged Navier-Stokes model [57,58] with a variety of turbulence models (e.g. k-, k-ω), as well as a second-order upwind scheme.…”

Partitioned Coupling vs. Monolithic Block-Preconditioning Approaches for Solving Stokes-Darcy Systems

“…4]. In the Stokes domain, a staggered grid is used for the quantities pressure and velocity, and the fluxes are approximated with an upwind scheme [16,22]. In summary, the discrete model, to be solved for every time step, has the form…”