Numerical coupling of Navier-Stokes and Darcy flow for soil-water evaporation [article]

Christoph Grüninger, Universität Stuttgart, Universität Stuttgart
2018
The objective of this work is to develop algorithms and provide a framework for an efficient coupling of free flow and porous-medium flow to simulate porous-medium-soil-water evaporation. The implementation must particularly be capable of simulating laminar free flows, be fast enough for applied research, and cover simulations in two and three dimensions with complex geometries. We introduce a model for a compositional non-isothermal free flow coupled with a two-fluid-phase compositional
more » ... thermal porous-medium flow. The free flow is modeled with the Navier-Stokes, component and energy transport equations. The porous-medium flow is modeled with compositional two-fluid-phase Darcy and energy transport equations. As the pressure has different orders in the free-flow and porous-medium-flow subdomains, the coupling is not straightforward. Although the simulation of the coupled flows is motivated by a laboratory experiment to measure soil-water evaporation caused by wind blowing over a water-filled porous bed, we intend to also explore its use in other applications The free flow is considered to be incompressible and laminar. We also assume that air and water follow nonlinear laws that describe their physical properties, and binary diffusion. Within the porous medium only creeping flows occur. Many quantities are averaged and used in a macroscopic sense. We use a formulation of two-phase Darcy law using the liquid saturation and the gas pressure as primary variables. The component mass fractions are calculated by Henry's law and the vapor pressure. The liquid phase may locally vanish leading to a variable switch, where the vapor mass fraction is tracked instead of the liquid saturation. We assume that a local thermodynamic equilibrium is valid everywhere within the domain, even across the interface. We follow the coupling concept proposed by Mosthaf et al. (2011), including the Beavers-Joseph-Saffman approach which has a sharp interface between the two subdomains. We use a cell-centered finite volume method (FVM) [...]
doi:10.18419/opus-9657 fatcat:pur4gklhorhexfhsoqijirgnie