Related papers: A finite-element model for computing fluid flow in…
We present a continuous and a discontinuous linear Finite Element method based on a predictor-corrector scheme for the numerical approximation of the Ericksen-Leslie equations, a model for nematic liquid crystal flow including a non-convex…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
Escaping of the liquid molecules from their liquid bulk into the vapour phase at the vapour-liquid interface is controlled by the vapour diffusion process, which nevertheless hardly senses the macroscopic shape of this interface. Here,…
In this paper we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing…
Reservoir simulators utilize numerical techniques to solve the governing equations of fluid flow in porous media and they are essential tool for oil and gas fields development. In practical reservoir simulation, the finite difference method…
An energy stable finite element scheme within arbitrary Lagrangian Eulerian (ALE) framework is derived for simulating the dynamics of millimetric droplets in contact with solid surfaces. Supporting surfaces considered may exhibit…
We present a unified variational mechanics framework for cavitating turbulent flows and structural motions via a stabilized finite element formulation. To model the finite mass transfer rate in cavitation phenomena, we employ the homogenous…
The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives…
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…
We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging-diverging tubes for Navier-Stokes…
Drop evaporation is a simple phenomena but still unclear concerning the mechanisms of evaporation. A common agreement of the scientific community based on experimental and numerical work evidences that most of the evaporation occurs at the…
This paper investigates finite-element modeling of a vertically damped free-standing rocking column. The paper first derives the nonlinear equation of motion for the coupled system and then compares the analytical solution with…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…
We present an efficient and accurate immersed boundary (IB) finite element (FE) method for internal flow problems with complex geometries (e.g., blood flow in the vascular system). In this study, we use a voxelized flow domain (discretized…
We propose an extension of the Maffettone-Minale (MM) model to predict the dynamics of an ellipsoidal droplet in a shear flow. The parameters of the MM model are traditionally retrieved in the framework of the perturbation theory for small…
We investigate theoretically and numerically the diffusion-limited evaporation of a liquid deposited on a fiber in two configurations: a sleeve and a axisymmetric barrel-shaped droplet. For a sleeve, the local flux depends on both the…
A model accounting for finite spatial dimensions of the deposit patterns in the evaporating sessile drops of colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…