Related papers: Numerical Experiments for Darcy Flow on a Surface …
This paper is part of a series developing $C^0$ finite element methods for fourth-order elliptic equations on polygonal domains. Here, we investigate how boundary conditions influence the design of effective $C^0$ schemes, specifically…
Stable and accurate finite element methods are presented for Darcy flow in heterogeneous porous media with an interface of discontinuity of the hydraulic conductivity tensor. Accurate velocity fields are computed through global or local…
Stokes flows are a type of fluid flow where convective forces are small in comparison with viscous forces, and momentum transport is entirely due to viscous diffusion. Besides being routinely used as benchmark test cases in numerical fluid…
We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the…
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…
The velocity, coupling term in the flow and transport problems, is important in the accurate numerical simulation or in the posteriori error analysis for adaptive mesh refinement. We consider Enhanced Velocity Mixed Finite Element Method…
Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field. The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.…
Cell blebs are protrusions of the cell membrane and can be instrumental for cell migration. We derive a continuum model for the mechanical and geometrical aspects of the onset of blebbing in terms of a force balance. It is abstract and…
The simulation of fluid flow problems, specifically incompressible flows governed by the Navier-Stokes equations (NSE), holds fundamental significance in a range of scientific and engineering applications. Traditional numerical methods…
In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of…
The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD)…
The objective of this study is to highlight the effect of porosity variation in a topology optimization process in the field of fluid dynamics. Usually a penalization term added to momentum equation provides to get material distribution.…
In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the…
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…
A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…
In this paper, a weak formulation of the discontinuous variable coefficient Poisson equation with interfacial jumps is studied. The existence, uniqueness and regularity of solutions of this problem are obtained. It is shown that the…
The Darcy model is based on a plethora of assumptions. One of the most important assumptions is that the Darcy model assumes the drag coefficient to be constant. However, there is irrefutable experimental evidence that viscosities of…
Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle-particle and particle-fluid interactions require an adequate representation but the computational cost has to be kept…
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…
First principles calculations based on density functional theory are having an incerasing impact on our understanding of molecule-surface interactions. For example, calculations of the multi-dimensional potential energy surface have…