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In this paper we consider a fully discrete numerical method for the unsteady Navier-Stokes equations on a smooth closed stationary surface in $\mathbb{R}^3$. We use the surface finite element method (SFEM) with a generalized Taylor-Hood…

Numerical Analysis · Mathematics 2025-12-03 Charles M. Elliott , Achilleas Mavrakis

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several CFD…

Numerical Analysis · Mathematics 2009-11-11 John B. Bell , Alejandro L. Garcia , Sarah A. Williams

A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. It is argued that this new pressure equation allows unifying…

Fluid Dynamics · Physics 2020-05-12 Adrien Toutant

We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes equations, and the fluid is subject to pure or partial slip…

Analysis of PDEs · Mathematics 2024-10-25 Yuanzhen Shao , Gieri Simonett , Mathias Wilke

We develop a mesh-based semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions recast as a non-linear transport problem for a momentum 1-form. A linearly implicit fully…

Numerical Analysis · Mathematics 2024-02-05 Wouter Tonnon , Ralf Hiptmair

Using an interpolant form for the gradient of a function of position, we write an integral version of the conservation equations for a fluid. In the appropriate limit, these become the usual conservation laws of mass, momentum and energy.…

Condensed Matter · Physics 2009-10-30 Victor Romero-Rochin , J. Miguel Rubi

The volume-filtering of the Navier-Stokes equations allows to consider the effect that particles have on the fluid without further assumptions, but closures arise of which the implications are not fully understood. In the present paper, we…

Fluid Dynamics · Physics 2024-11-20 Max Hausmann , Victor Chéron , Fabien Evrard , Berend van Wachem

We derive the gas dynamics equations considering changes of velocity distribution function on the scale of a molecule free path. We define the molecule velocity distribution function in a specific form so that only molecule velocities after…

General Physics · Physics 2007-05-23 Alexander V. Kochin

The micropolar fluid system is a model based on the Navier-Stokes equations which considers two coupled variables: the velocity field $\vec u$ and the microrotation field $\vec\omega$. Assuming an additional condition over the variable…

Analysis of PDEs · Mathematics 2024-06-06 Diego Chamorro , David Llerena

The Navier-Stokes equation contains two terms which have been subjected to slight modification: (a) the viscosity term depends of time (the viscosity in average on time is zero, but its variance is non-zero), (b) the pressure gradient…

Quantum Physics · Physics 2016-08-09 Valeriy I. Sbitnev

Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air. Due to the importance of Navier-Stokes equations, the development on efficient numerical schemes is important…

Fluid Dynamics · Physics 2022-07-21 Rui Zhang , Peiyan Hu , Qi Meng , Yue Wang , Rongchan Zhu , Bingguang Chen , Zhi-Ming Ma , Tie-Yan Liu

A new exact solution of the Navier-Stokes equation is derived for the compressible flows which are far from equilibrium in the limit of extremely low shear viscosity and relatively large volume viscosity. The closed description of the…

Fluid Dynamics · Physics 2019-03-05 Sergey G. Chefranov , Artem S. Chefranov

We introduce a residual-based stabilized formulation for incompressible Navier-Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf-sup stable spaces with $H^1$-conforming pressure…

Numerical Analysis · Mathematics 2019-11-07 John A. Evans , David Kamensky , Yuri Bazilevs

In the theory of the Navier-Stokes equations, the viscous fluid in incompressible flow is modelled as a homogeneous and dense assemblage of constituent "fluid particles" with viscous stress proportional to rate of strain. The crucial…

Fluid Dynamics · Physics 2022-08-23 Wennan Zou

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and…

Numerical Analysis · Mathematics 2018-05-15 Alexander Lozovskiy , Maxim A. Olshanskii , Yuri V. Vassilevski

A model is developed describing the approach to a finite-time singularity of the Navier-Stokes equations for two interacting vortices. The model is derived from a combination of the Biot-Savart law and an equation describing the evolution…

Fluid Dynamics · Physics 2018-11-21 Keith Moffatt , Yoshifumi Kimura

In this paper we discuss the formulation of the fuctuating Navier-Stokes (FNS) equations for multi-species, non-reactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial…

Fluid Dynamics · Physics 2014-01-17 Kaushik Balakrishnan , Alejandro L. Garcia , Aleksandar Donev , John B. Bell

The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…

Fluid Dynamics · Physics 2017-01-25 Melissa Morris

Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires to derive constitutive relations for…

Statistical Mechanics · Physics 2015-05-27 J. Javier Brey , P. Maynar , M. I. Garcia de Soria

We derive a novel lattice Boltzmann scheme, which uses a pressure correction forcing term for approximating the volume averaged Navier-Stokes equations (VANSE) in up to three dimensions. With a new definition of the zeroth moment of the…

Numerical Analysis · Mathematics 2023-07-19 Fedor Bukreev , Stephan Simonis , Adrian Kummerländer , Julius Jeßberger , Mathias J. Krause