相关论文: An Observation On The Uniform Preconditioners For …
Mathematical modelling of coupled flow systems containing a free-flow region in contact with a porous medium is challenging, especially for arbitrary flow directions to the fluid--porous interface. Transport processes in the free flow and…
In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes…
We present a new approach for the mechanically consistent modelling and simulation of fluid-structure interactions with contact. The fundamental idea consists of combining a relaxed contact formulation with the modelling of seepage through…
This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate $LDL^t$…
The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into account memory effects. At the…
In the presence of strong heterogeneities, it is well known that the use of explicit schemes for the transport of species in a porous medium suffers from severe restrictions on the time step. This has led to the development of implicit…
We propose an unified algebraic approach for static condensation and hybridization, two popular techniques in finite element discretizations. The algebraic approach is supported by the construction of scalable solvers for problems involving…
We study a diffuse interface model describing the motion of two viscous fluids driven by the surface tension in a Hele-Shaw cell. The full system consists of the Cahn-Hilliard equation coupled with the Darcy's law. We address the physically…
We study numerical methods for solving reactive transport problems in porous media that allow a separation of transport and chemistry at the software level, while keeping a tight numerical coupling between both subsystems. After recalling…
Matter at intermediate baryon densities and low temperatures is notoriously hard to tackle theoretically. Whereas lattice methods cannot cover more than rather small densities, perturbative methods are only applicable at much higher…
A combination of block-Jacobi and deflation preconditioning is used to solve a high-order discontinuous element-based collocation discretization of the Schur complement of the Poisson-Neumann system as arises in the operator splitting of…
In this paper we devise and analyze a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock…
We consider one-level additive Schwarz preconditioners for a family of Helmholtz problems with absorption and increasing wavenumber $k$. These problems are discretized using the Galerkin method with nodal conforming finite elements of any…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a…
In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…
Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work we consider a simplified model problem of a 3d-1d coupling and the main objective is to…
We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous…
Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the…