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Related papers: A conservative hybrid method for Darcy flow

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This paper presents a family of spatial discretisations of the nonlinear rotating shallow-water equations that conserve both energy and potential enstrophy. These are based on two-dimensional mixed finite element methods and hence, unlike…

Numerical Analysis · Mathematics 2015-06-16 Andrew T. T. McRae , Colin J. Cotter

We develop a novel Hybrid High-Order method for the simulation of Darcy flows in fractured porous media. The discretization hinges on a mixed formulation in the bulk region and on a primal formulation inside the fracture. Salient features…

Numerical Analysis · Mathematics 2017-12-01 Florent Chave , Daniele Di Pietro , Luca Formaggia

We present an alternative "encapsulated" formulation of the Selective Frequency Damping method for finding unstable equilibria of dynamical systems, which is particularly useful when analysing the stability of fluid flows. The formulation…

Fluid Dynamics · Physics 2015-06-18 Bastien E. Jordi , C. J. Cotter , Spencer J. Sherwin

We propose two different discrete formulations for the weak imposition of the Neumann boundary conditions of the Darcy flow. The Raviart-Thomas mixed finite element on both triangular and quadrilateral meshes is considered for both methods.…

Numerical Analysis · Mathematics 2021-04-06 Erik Burman , Riccardo Puppi

A solution technique is proposed for flows in porous media that guarantees local conservation of mass. We first compute a flux field to balance the mass source and then exploit exact co-chain complexes to generate a solenoidal correction. A…

Numerical Analysis · Mathematics 2022-06-01 Wietse M. Boon , Alessio Fumagalli

The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated.…

Disordered Systems and Neural Networks · Physics 2009-11-13 Tim Rogers , Isaac Perez Castillo

We design a numerical approximation of a system of partial differential equations modelling the miscible displacement of a fluid by another in a porous medium. The advective part of the system is discretised using a characteristic method,…

Numerical Analysis · Mathematics 2018-08-23 Hanz Martin Cheng , Jerome Droniou

A linear system of differential equations describing a joint motion of a thermoelastic porous body with a sufficiently large Lame's constants (absolutelty rigid body) and a thermofluid, occupying porous space, is considered. The rigorous…

Analysis of PDEs · Mathematics 2007-05-23 Anvarbek Meirmanov

Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our…

Numerical Analysis · Mathematics 2017-07-18 Wietse M. Boon , Jan M. Nordbotten , Ivan Yotov

In this paper, we develop a discretization for the non-linear coupled model of classical Darcy-Forchheimer flow in deformable porous media, an extension of the quasi-static Biot equations. The continuous model exhibits a generalized…

Numerical Analysis · Mathematics 2021-05-24 Jakub Wiktor Both , Jan Martin Nordbotten , Florin Adrian Radu

We present and discuss a novel approach to deal with conservation properties for the simulation of nonlinear complex porous media flows in the presence of: 1) multiscale heterogeneity structures appearing in the elliptic-pressure-velocity…

Numerical Analysis · Mathematics 2020-06-15 Juan Galvis , Eduardo Abreu , Ciro Diaz , Jonh Perez

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…

Numerical Analysis · Mathematics 2021-02-02 Guido Kanschat , Raytcho Lazarov , Youli Mao

We investigate the discretization of Darcy flow through fractured porous media on general meshes. We consider a hybrid dimensional model, invoking a complex network of planar fractures. The model accounts for matrix-fracture interactions…

Numerical Analysis · Mathematics 2015-09-08 K. Brenner , J. Hennicker , R. Masson , P. Samier

In this paper, we propose a physics-preserving multiscale method to solve an immiscible two-phase flow problem, which is modeled as a coupling system consisting of Darcy's law and mass conservation equations. We use a new Physics-preserving…

Numerical Analysis · Mathematics 2022-12-13 Yiran Wang , Eric Chung , Shuyu Sun

We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite…

Numerical Analysis · Mathematics 2016-10-19 Peter Knabner , Gerhard Summ

In this paper we consider modifications to Darcy's equation wherein the drag coefficient is a function of pressure, which is a realistic model for technological applications like enhanced oil recovery and geological carbon sequestration. We…

Numerical Analysis · Computer Science 2010-04-12 K. B. Nakshatrala , K. R. Rajagopal

We study the slightly compressible Darcy-Forchheimer equations modeling gas flow in porous media, particularly in applications related to combustion processes. The equations are discretized in time using the backward Euler method and in…

Numerical Analysis · Mathematics 2026-04-16 Laura Portero , Andrés Arrarás , Francisco J. Gaspar , Florin A. Radu

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…

Numerical Analysis · Mathematics 2022-03-02 Erik Burman , Miguel A. Fernández , Stefan Frei , Fannie M. Gerosa

We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of…

Numerical Analysis · Mathematics 2022-04-08 Weizhu Bao , Harald Garcke , Robert Nurnberg , Quan Zhao

A conservative flux postprocessing algorithm is presented for both steady-state and dynamic flow models. The postprocessed flux is shown to have the same convergence order as the original flux. An arbitrary flux approximation is projected…

Numerical Analysis · Mathematics 2017-10-20 Lars H. Odsæter , Mary F. Wheeler , Trond Kvamsdal , Mats G. Larson