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...

An H(div) conforming mixed finite element method has been proposed for the coupled Darcy-Stokes flow in [30], which imposes normal continuity on the velocity field strongly across the Darcy-Stokes interface. Here, we develop an a posteriori error estimator for this H(div) conforming mixed method, and prove its global reliability and efficiency. Due to the strong coupling on the interface, speci...

This paper presents a new approach to verify accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniques to identify numerical pollution, check the performance of adaptive meshes, and verify numerical solutions. We demonstrate performance of this methodology on problems from flow thorough porous media. However, one c...

Motivated by casting of fresh concrete in reinforced concrete structures, we introduce a numerical model of a steady-state non-Newtonian fluid flow through a porous domain. Our approach combines homogenization techniques to represent the reinforced domain by the Darcy law with an interfacial coupling of the Stokes and Darcy flows through the Beavers-Joseph-Saffman conditions. The ensuing two-sc...

In this paper, we first recall a previous favourable experience with the Schwarz type domain decomposition methods applied to problems of heat flow and elasticity [9, 11, 12] and then discuss a possible use of these methods for solving Darcy flow problems.