This paper introduces two stabilization schemes for the Least Squares Commutator (LSC) preconditioner developed by Elman, Howle, Shadid, Shuttleworth and Tuminaro [SIAM J. Sci. Comput., 27, 2006, pp. 1651–1668] for the incompressible Navier-Stokes equations. This preconditioning methodology is one of several choices that are effective for Navier-Stokes equations, and it has the advantage of bei...

In this article, we propose to study two issues associated with the use of the incremental projection method for solving the incompressible Navier-Stokes equation. The first one is the combination of this time splitting algorithm with an adaptive local refinement method. The second one is the reduction of spurious velocities due to the right-hand side of the momentum balance. We propose a new v...

In this paper, we analyze a tamed 3D Navier-Stokes equation in uniform C-domains (not necessarily bounded), which obeys the scaling invariance principle, and prove the existence and uniqueness of strong solutions to this tamed equation. In particular, if there exists a bounded solution to the classical 3D Navier-Stokes equation, then this solution satisfies our tamed equation. Moreover, the exi...

In this paper we address the existence, the asymptotic behavior and stability in L and L, 3 2 < p ≤ ∞, for solutions to the steady state 3D Navier-Stokes equations with possibly very singular external forces. We show that under certain smallness conditions of the forcing term there exists solutions to the stationary Navier-Stokes equations in L spaces, and we prove the stability of these soluti...

We give two results that indicate that the relaxation time for the flow governed by the Navier-Stokes-Voigt (NSV) model is sinificantly larger than for the Navier-Stokes equations. We first show that for the Green-Taylor vortex decay problem, NSV admits an exact solution which has a significantly larger half life than for true fluid flow. Second, we observe in a channel flow test that NSV provi...

A comparison is made between the Hagen-Poiseuille flow in rigid tubes and networks on one side and the time-independent one-dimensional Navier-Stokes flow in elastic tubes and networks on the other. Analytical relations, a Poiseuille network flow model and two finite element Navier-Stokes one-dimensional flow models have been developed and used in this investigation. The comparison highlights t...

This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier–Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers’s equa...

This article describes a new numerical solver for the Navier-Stokes equations. The proposed solver is written in Python which is a newly developed language. The Python packages are built to solve the Navier-Stokes equations with existing libraries. We have created discretized coefficient matrices from systems of the Navier-Stokes equations by the finite difference method. In addition we focus o...

A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations. The time discretization of the penalty Navier-Stokes equations is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Navier-Stokes equations is based on a finite element space pair (Xh,Mh) which satisfies some approximate assumpt...

We investigate the self-similar solutions to the isothermal compressible Navier–Stokes equations. The aim of this paper is to show that there exist neither forward nor backward self-similar solutions with finite total energy. This generalizes the results for the incompressible case in Nečas, J., Ru̇žička, M. & Šverák, V. (1996, On Leray’s self-similar solutions of the Navier-Stokes equations. Ac...