Related papers: On convergence of Chorin's projection method to a …
We study Chorin's projection method combined with a finite element spatial discretization for the time-dependent incompressible Navier-Stokes equations. The scheme advances the solution in two steps: a prediction step, which computes an…
Kuroki and Soga [Numer. Math. 2020] proved that a version of Chorin's fully discrete projection method, originally introduced by A. J. Chorin [Math. Comp. 1969], is unconditionally solvable and convergent within an arbitrary fixed time…
We analyze a second-order projection method for the incompressible Navier-Stokes equations on bounded Lipschitz domains. The scheme employs a Backward Differentiation Formula of order two (BDF2) for the time discretization, combined with…
This paper deals with the approximation of the weak solutions of the incompressible Navier Stokes Fourier system. In particular it extends the artificial compressibility method for the Leray weak solutions of the Navier Stokes equation,…
We prove the ill-posedness for the Leray-Hopf weak solutions of the incompressible and ipodissipative Navier-Stokes equations, when the power of the diffusive term $(-\Delta)^\gamma$ is $\gamma < \frac{1}{3}$. We construct infinitely many…
The present paper addresses the convergence of a first order in time incremental projection scheme for the time-dependent incompressible Navier-Stokes equations to a weak solution, without any assumption of existence or regularity…
We prove the convergence of an incremental projection numerical scheme for the time-dependent incompressible Navier--Stokes equations, without any regularity assumption on the weak solution. The velocity and the pressure are discretised in…
This paper provides mathematical analysis of an elementary fully discrete finite difference method applied to inhomogeneous (non-constant density and viscosity) incompressible Navier-Stokes system on a bounded domain. The proposed method…
In this paper we study the Leray weak solutions of the incompressible Navier Stokes equation in an exterior domain.We describe, in particular, an hyperbolic version of the so called artificial compressibility method investigated by…
We prove the existence and uniqueness of weak solutions of the inhomogeneous incompressible Navier--Stokes equations without vacuum using the relative energy method. We present a novel and direct proof of the existence of weak solutions…
In this paper we study how to approximate the Leray weak solutions of the incompressible Navier Stokes equation. In particular we describe an hyperbolic version of the so called artificial compressibility method investigated by J.L.Lions…
We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus $g(\mathcal{S})$. The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding…
We present a variational approach for the construction of Leray-Hopf solutions to the non-Newtonian Navier-Stokes system. Inspired by the work [42] on the corresponding Newtonian problem, we minimise certain stabilised Weighted…
We consider a projection method for time-dependent incompressible Navier-Stokes equations with a total pressure boundary condition. The projection method is one of the numerical calculation methods for incompressible viscous fluids often…
A well-established numerical approach to solve the Navier--Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved,…
Using the concept of stationary statistical solution, which generalizes the notion of invariant measure, it is proved that, in a suitable sense, time averages of almost every Leray-Hopf weak solution of the three-dimensional incompressible…
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…
The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous…
We prove the existence of the weak solutions to the compressible Navier--Stokes system with barotropic pressure $p(\varrho)=\varrho^\gamma$ for $\gamma\geq 9/5$ in three space dimension. The novelty of the paper is the approximation scheme…
We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…