Related papers: An Eulerian finite element method for the lineariz…
We implement a stabilized finite element method for steady Darcy-Brinkman-Forchheimer model within the continuous Galerkin framework. The nonlinear fluid model is first linearized using a standard \textit{Newton's method. The sequence of…
This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier--Stokes equations expressed in…
Convergence results for the immersed boundary method applied to a model Stokes problem with the homogeneous Dirichlet boundary condition are presented. As a discretization method, we deal with the finite element method. First, the immersed…
In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…
In this work, we design and analyze semi/fully-discrete virtual element approximations for the time-dependent Navier--Stokes-Cahn--Hilliard equations, modeling the dynamics of two-phase incompressible fluid flows with diffuse interfaces. A…
This paper exposes how to obtain a relation that have to be hold for all free--divergence velocity fields that evolve according to Navier--Stokes equations. However, checking the violation of this relation requires a huge computational…
We present a space-time Cut Finite Element Method (CutFEM) for the time-dependent Navier-Stokes equations involving two immiscible incompressible fluids with different viscosities, densities, and with surface tension. The numerical method…
We present a second-order monolithic method for solving incompressible Navier--Stokes equations on irregular domains with quadtree grids. A semi-collocated grid layout is adopted, where velocity variables are located at cell vertices, and…
This manuscript introduces an advanced numerical approach for the integration of incompressible Navier-Stokes (NS) equations using a Time Series Expansion (TSE) method within a Finite Element Method (FEM) framework. The technique is…
Solution of the Navier-Stokes equations with initial conditions (Cauchy problem) for 2D and 3D cases was obtained in the convergence series form by iterative method using Fourier and Laplace transforms in paper $\cite{TT02}$. For several…
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…
We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in…
We prove the existence and uniqueness of solutions to the time-dependent incompressible Navier-Stokes equations with a free-boundary governed by surface tension. The solution is found using a topological fixed-point theorem for a nonlinear…
We introduce an unfitted finite element method with Lagrange-multipliers to study an Eulerian time stepping scheme for moving domain problems applied to a model problem where the domain motion is implicit to the problem. We consider a…
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,…
In this work, we develop a high-order pressure-robust method for the rotation form of the stationary incompressible Navier-Stokes equations. The original idea is to change the velocity test functions in the discretization of trilinear and…
In this paper, we construct a novel Eulerian-Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the…
Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to…
We obtain error bounds for a modified Chorin-Teman (Euler non-incremental) method for non inf-sup stable mixed finite elements applied to the evolutionary Navier-Stokes equations. The analysis of the classical Euler non-incremental method…
A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless…