English
Related papers

Related papers: Pressure-induced locking in mixed methods for time…

200 papers

A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes…

Fluid Dynamics · Physics 2013-09-11 Maciej Balajewicz , Earl Dowell , Bernd Noack

We identify a norm on the pressure variable in the Stokes equation that allows us to prove a continuous inf-sup condition with a constant independent of the domain's aspect ratio. This is in contrast to the standard inf-sup constant, which…

Numerical Analysis · Mathematics 2025-10-29 Espen Sande , Timo Koch , Miroslav Kuchta , Kent-Andre Mardal

We prove existence of global in time weak solutions to a compressible two-fluid Stokes system with a single velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an…

Analysis of PDEs · Mathematics 2018-12-05 Didier Bresch , Piotr B. Mucha , Ewelina Zatorska

Pressure Poisson equation (PPE) reformulations of the incompressible Navier-Stokes equations (NSE) replace the incompressibility constraint by a Poisson equation for the pressure and a suitable choice of boundary conditions. This yields a…

Numerical Analysis · Mathematics 2023-08-16 Rodolfo Ruben Rosales , Benjamin Seibold , David Shirokoff , Dong Zhou

The aim of this article is to justify mathematically, in the two-dimensional periodic setting, a generalization of a two-phase model with pressure dependent viscosity first proposed by A. Lefebvre-Lepot and B. Maury to describe a system in…

Analysis of PDEs · Mathematics 2015-08-24 Charlotte Perrin

We present a system of Navier-Stokes type that describes the dynamics of several spherical bubbles of gas in a liquid. It is derived from a more complete model, where the bubbles are seen as inclusions of gas of homogeneous barotropic…

Analysis of PDEs · Mathematics 2025-07-30 Cosmin Burtea , David Gérard-Varet

In this paper, we extend considerably the global existence results of entropy-weak solutions related to compressible Navier-Stokes system with density dependent viscosities obtained, independently (using different strategies), by Vasseur-Yu…

Analysis of PDEs · Mathematics 2019-05-08 Didier Bresch , Alexis Vasseur , Cheng Yu

First order semi-linear coupling of scalar hypoelliptic equations of second order leads to a natural class of incompressible Navier Stokes equation systems, which encompasses systems with variable viscosity and essentially Navier Stokes…

Analysis of PDEs · Mathematics 2013-08-13 Joerg Kampen

In this paper, several projection method based preconditioners for various incompressible flow models are studied. In particular, we are interested in the theoretical analysis of a pressure-correction projection method based preconditioner…

Numerical Analysis · Mathematics 2013-12-12 Mingchao Cai

We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations discretized on staggered (MAC) grids. The scheme is based on finite difference approximations…

Numerical Analysis · Mathematics 2025-12-24 Andreu Martorell , Pep Mulet , Dionisio F. Yáñez

The Navier-Stokes equations in the primitive formulation for incompressible flow describe the evolution of velocity and pressure, without recourse to vorticity. We show that, beyond the finite Leray-Hopf regularity interval, every…

Analysis of PDEs · Mathematics 2021-03-30 F. Lam

We investigate the inertial limit of the compressible Navier--Stokes system posed on the $3$-dimensional torus, and allowing for regions of vacuum. Considering global-in-time finite-energy weak solutions of a scaled system, we rigorously…

Analysis of PDEs · Mathematics 2026-03-13 Cheng Yu

We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Maxwell-Stefan closure approach. Mechanical forces result into…

Analysis of PDEs · Mathematics 2020-01-27 Dieter Bothe , Pierre-Etienne Druet

In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that this kind of methods lead to arbitrarily ill-conditioned systems. In order to solve this issue, we…

Numerical Analysis · Mathematics 2021-09-30 Santiago Badia , Alberto F. Martín , Francesc Verdugo

This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles…

Numerical Analysis · Mathematics 2023-04-06 Yuwen Li , Ludmil Zikatanov

This article is devoted to the well-posedness of the stochastic compressible Navier Stokes equations. We establish the global existence of an appropriate class of weak solutions emanating from large inital data, set within a bounded domain.…

Analysis of PDEs · Mathematics 2015-04-07 Scott Smith

The work described here shows that the known variational principle for the Navier-Stokes equations and the adjoint system can be modified to produce a set of Euler-Lagrange variational equations which have the same order and same solution…

Analysis of PDEs · Mathematics 2017-05-04 Shahrdad G. Sajjadi

We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong…

Analysis of PDEs · Mathematics 2018-12-07 Ondřej Kreml , Šárka Nečasová , Tomasz Piasecki

This project work report provides a full solution of simplified Navier Stokes equations for The Incompressible Couette Problem. The well known analytical solution to the problem of incompressible couette is compared with a numerical…

Computational Physics · Physics 2007-05-23 Maciej Matyka

We construct non-unique Leray solutions of the forced Navier-Stokes equations in bounded domains via gluing methods. This demonstrates a certain locality and robustness of the non-uniqueness discovered by the authors in [1].

Analysis of PDEs · Mathematics 2023-09-18 Dallas Albritton , Elia Bruè , Maria Colombo