We consider a multidimensional model for the dynamic combustion of compressible reacting fluids formulated by the Navier Stokes equations in Euler coordinates. For the chemical model we consider a one way irreversible chemical reaction governed by the Arrhenius kinetics. The existence of globally defined weak solutions of the Navier-Stokes equations for compressible reacting fluids is establish...

Formulated in terms of velocity, pressure and the extra stress tensor, the incompressible Navier-Stokes equations are discretized by stabilized finite element methods. The stabilized methods proposed are analyzed for a linear model and extended to the Navier-Stokes equations. The numerical tests performed confirm the good stability characteristics of the methods. These methods are applicable to...

On regularity of stationary Stokes and Navier-Stokes equations near boundary KYUNGKEUN KANG Received: date / Revised version: date – c Springer-Verlag 2001 Abstract. We obtain local estimates of the steady-state Stokes system “without pressure” near boundary. As an application of the local estimates, we prove the partial regularity up to the boundary for the stationary Navier-Stokes equations i...

We study in this article both the structure and the structural evolution of the solutions of 2-D Navier-Stokes equations with periodic boundary conditions and the evolution of their solutions. First the structure of all eigenvectors of the corresponding Stokes problem is classified using a block structure, and is linked to the typical structure of the Taylor vortices. Then the structure of the ...

We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection method to deal with the incompressibility constraint. The stability of the scheme has been proven in [15]. We infer from it its convergence. Mathematics Subject ...

The aim of this dissertation is to study stochastic Navier-Stokes equations with a fractional Brownian motion noise. The second chapter will introduce the background results on fractional Brownian motions and some of their properties. The third chapter will focus on the Stokes operator and the semigroup generated by this operator. The Navier-Stokes equations and the evolution equation setup wil...

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompre...

We address the problem of the uniqueness of the particle trajectories corresponding to a weak solution of the two-dimensional Navier-Stokes equations with square integrable initial condition and regular enough forcing function. In order to do this we obtain an estimate for H-norm of the weak solutions of the Navier-Stokes equations and show that t‖D3/2u‖ is bounded which provides a bound on the...

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...

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...