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Presure Boundary Conditions in the Collocated Finite-Volume Method for the Steady Navier–Stokes Equations
AbstractThe pressure boundary conditions for the steady-state solution of the incompressible Navier–Stokes equations with the collocated...
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A Posteriori Error Analysis of a Mixed Finite Element Method for the Coupled Brinkman–Forchheimer and Double-Diffusion Equations
In this paper we consider a partially augmented fully-mixed variational formulation that has been recently proposed for the coupling of the...
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Mathematical modeling of mixed convective MHD Falkner-Skan squeezed Sutterby multiphase flow with non-Fourier heat flux theory and porosity
In a wide variety of mechanical and industrial applications, e.g., space cooling, nuclear reactor cooling, medicinal utilizations (magnetic drug...
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A Combined Mixed Hybrid and Hybridizable Discontinuous Galerkin Method for Darcy Flow and Transport
A combined hybrid mixed and hybridizable discontinuous Galerkin method is formulated for the flow and transport equations. Convergence of the method...
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WELL-POSEDNESS OF A NONLINEAR INTERFACE PROBLEM DESCRIBED BY HEMIVARIATIONAL INEQUALITIES VIA BOUNDARY INTEGRAL OPERATORS
This paper is devoted to the well-posedness of a novel nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission...
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Bifurcations of drops and bubbles propagating in variable-depth Hele-Shaw channels
The steady propagation of air bubbles through a Hele-Shaw channel with either a rectangular or partially occluded cross section is known to exhibit...
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A HDG Method for Elliptic Problems with Integral Boundary Condition: Theory and Applications
In this paper, we address the study of elliptic boundary value problems in presence of a boundary condition of integral type (IBC) where the...
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The impact of imposed Couette flow on the stability of pressure-driven flows over porous surfaces
We present linear stability analysis of a pressure-driven flow in a fluid-layer overlaying porous media in the presence of a Couette component...
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Convection in a rectangular enclosure with internally heated porous medium: impact of boundary conditions
The present work is focussed on analyzing the stability of fluid within the porous structure, accounting for constant internal heat generation by...
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A Parallel Robin–Robin Domain Decomposition Method based on Modified Characteristic FEMs for the Time-Dependent Dual-porosity-Navier–Stokes Model with the Beavers–Joseph Interface Condition
In this paper, we propose and analyze the parallel Robin–Robin domain decomposition method based on the modified characteristic finite element method...
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A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation
In this paper we study the a posteriori error estimates for the time dependent Navier-Stokes system coupled with the convection-diffusion-reaction...
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Second-order schemes for axisymmetric Navier–Stokes–Brinkman and transport equations modelling water filters
Soil-based water filtering devices can be described by models of viscous flow in porous media coupled with an advection–diffusion–reaction system...
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Gaussian process hydrodynamics
We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and...
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Subproblems Individually
In this section the existence and uniqueness of solutions of the involved subproblems are proved. Besides the Laplace equation this includes the...
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A posteriori error estimate for the non-stationary concentration equation coupled with the Darcy system discretized by the Raviart–Thomas finite element
This article focuses on discretizing the convection–diffusion–reaction equation (concentration or heat), which is time-dependent and coupled with the...
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Flow and transport in fractured poroelastic media
We study flow and transport in fractured poroelastic media using Stokes flow in the fractures and the Biot model in the porous media. The Stokes–Biot...
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Fully-Implicit Collocated Finite-Volume Method for the Unsteady Incompressible Navier–Stokes Problem
This article introduces a collocated finite-volume method for the incompressible Navier–Stokes equations. Based on the linearity assumption of the...
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A Divergence-Free Petrov–Galerkin Immersed Finite Element Method for Stokes Interface Problem
The paper proposes a Petrov–Galerkin immersed finite element (PGIFE) method for solving Stokes interface problems. We employ the uniform mesh which...
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A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes
In this paper, we present a divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes. The velocity and the...