Mathematical analysis of the Navier-Stokes/Darcy coupling
نویسندگان
چکیده
We consider a differential system based on the coupling of the Navier-Stokes and Darcy equations for modeling the interaction between surface and subsurface flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov-Poincaré operators, and we prove its wellposedness.
منابع مشابه
Coupling Stokes--Darcy Flow with Transport
A mathematical and numerical model describing chemical transport in a Stokes– Darcy flow system is discussed. The flow equations are solved through domain decomposition using classical finite element methods in the Stokes region and mixed finite element methods in the Darcy region. The local discontinuous Galerkin (LDG) method is used to solve the transport equation. Models dealing with couplin...
متن کاملNumerical analysis of the Navier-Stokes/Darcy coupling
We consider a differential system based on the coupling of the Navier-Stokes and Darcy equations for modeling the interaction between surface and porousmedia flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov-Poincaré operators, and we prove its wellposedness. We propose and analyze iterative methods to solve a conforming finite element appro...
متن کاملCoupling DuMuX and DUNE-PDELab to investigate evaporation at the interface between Darcy and Navier-Stokes flow
An implementation of a coupled Navier-Stokes/Darcy model based on different Dune discretization modules is presented. The Darcy model is taken from DuMux, the Navier-Stokes model is implemented on top of Dune-PDELab, and the coupling is done with help of Dune-MultiDomain together with some project-specific auxiliary code. The Navier-Stokes model features one fluid phase, the Darcy model two flu...
متن کاملDomain Decomposition Methods for the Coupling of Surface and Groundwater Flows
The purpose of this thesis is to investigate, from both the mathematical and numerical viewpoint, the coupling of surface and porous media flows, with particular concern on environmental applications. Domain decomposition methods are applied to set up effective iterative algorithms for the numerical solution of the global problem. To this aim, we reformulate the coupled problem in terms of an i...
متن کاملError studies of the Coupling Darcy-Stokes system with velocity-pressure formulation
In this paper we study the Coupling Darcy-Stokes Systems. We establish a coupled variational formulation with the velocity and the pressure. The velocity is approximated with curl conforming finite elements and the pressure with standard continuous elements. We establish optimal a priori and a posteriori error estimates. We conclude our paper with some numerical simulations.
متن کامل