For increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier–Stokes equations lose accuracy. These inaccuracies are attributed primarily to the linear approximations of the stress and heat flux terms in the Navier– Stokes equations. The inclusion of higher order terms, such as Burnett, or high-order moment equations, could improve the predictive capabilit...

In this project report I present my research and accompanying implementation of the unconditionally stable Navier-Stokes partial differential equation (PDE) solver presented to the computer graphics community by Jos Stam at the 1999 SIGGRAPH conference [Stam 1999]. I give a brief introduction to computational fluid dynamics (CFD), the governing Navier-Stokes equations and an overview of previou...

1. Introduction. Recently A. Chorin has found a numerical scheme for solving the Navier-Stokes equations which has the pleasing feature of not breaking down at high Reynolds numbers R [5]. The purpose of this announcement is to present a formula «2) below) which is designed to establish the convergence of Chorin's time step iteration procedure, assuming that the relevant equations (heat equatio...

Equation (1) is just Newton’s law f = ma for a fluid element subject to the external force f = (fi(x, t))1 i n and to the forces arising from pressure and friction. Equation (2) just says that the fluid is incompressible. For physically reasonable solutions, we want to make sure u(x, t) does now grow large as |x| → ∞. Hence, we will restrict attention to forces f and initial conditions u◦ that ...

a novel computational fluid dynamics and molecular kinetic theory (cfd-mk) method was developed to simulate the impingement of a nanodroplet onto a solid surface. a numerical solution of the navier–stokes equation using a volume-of-fluid (vof) technique was used to model nanodroplet deformation. dynamic contact angle during droplet impact was obtained by molecular kinetic theory. this dynamic c...

We establish a representation of the solution of 3d Navier-Stokes equations in the space Φ(α, α) using sums over rooted trees. We study the convergence properties of this series recovering in a simplified manner some results obtained recently by Sinai and other known results. The series representation make sense also in the critical case where there exists global solutions for small initial data.

The equations of motion of conducting fluid in a magnetic field are formulated. These consist of three sets. First is the mass conservation equation, second Navier Stokes equation which is Newton’s second law taking into account the force of magnetic field on moving charges. The electrical field effects are neglected as is usually done in MHD. The third set is Maxwell’s equation especially to m...

A computational procedure based on a divergence-free H(div) method is presented for the Stokes and Navier-Stokes equations in this article. This method is designed to find velocity approximation in an exact divergence-free subspace of the corresponding H(div) finite element space. That is, the continuity equation is strongly enforced a priori and the pressure is eliminated from the calculation....

Keywords: Rotating Navier–Stokes equations Exterior domain Boundary integral method Finite element approximation a b s t r a c t In this paper, we apply the boundary integral method to the linearized rotating Navier– Stokes equations in exterior domain. Introducing some open ball which decomposes the exterior domain into a finite domain and an infinite domain, we obtain a coupled problem by the...

In this paper we establish a number of implications between various qualitative and quantitative versions of the global regularity problem for the Navier-Stokes equations, in the periodic, smooth finite energy, smooth H, Schwartz, or mild H categories, and with or without a forcing term. In particular, we show that if one has global well-posedness in H for the periodic Navier-Stokes problem wit...