In this paper, we propose a new numerical scheme for the coupled Stokes-Darcy model with Beavers-Joseph-Saffman interface condition. We use weak Galerkin method to discretize Stokes equation and mixed finite element Darcy equation. A discrete inf-sup condition is proved optimal error estimates are also derived. Numerical experiments validate theoretical analysis.

We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes--Darcy problem. Three different formulations their discretizations in terms of conforming nonconforming finite element methods volume are considered. In each case, robust preconditioners derived using a unified theoretical framework. particular, suggested utilize operators fractional Sobolev spac...

Due to the long-term fluid-solid interactions in waterflooding, the tremendous variation of oil reservoir formation parameters will lead to the widespread evolution of preferential flow paths, thereby preventing the further enhancement of recovery efficiency because of unstable fingering and premature breakthrough. To improve oil recovery, the characterization of preferential flow paths is esse...

for non-darcy flow in submerged porous media a one- dimensional mathematical model has been developed. rockfill detention dams are one of these porous media that comprised of relatively homogenous coarse rockfill which can be used to reduce flood discharge and hydrograph peak. in this research the focus was on the rockfill detention dams in submerged condition. the existence of overtopping rock...

A reduced basis Darcy-Stokes finite element heterogeneous multiscale method (RBDS-FE-HMM) is proposed for the Stokes problem in porous media. The multiscale method is based on the Darcy-Stokes finite element heterogeneous multiscale method (DS-FE-HMM) introduced in [A. Abdulle, O. Budáč, Multiscale Model. Simul. 13 (2015)] that couples a Darcy equation solved on a macroscopic mesh, with missing...

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...

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.

We consider a stationary two-phase Stefan problem with convection. The problem is governed by a coupled system involving a nonlinear Darcy law and the energy balance equation with second member in L 1. We prove existence of at least one weak solution of the problem, using the penalty method and the Schauder xed point principle.

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.