Upwind schemes for the Euler and Navier-Stokes equations may be broadly classified into two distinct classes: those based directly on the macroscopic Navier-Stokes equations and those based indirectly on the Navier-Stokes equations via the Boltzmann equation. The former, conventional approach represents the majority of current research. However, recently gas-kinetic methods have gained attentio...

In this paper, we study the dynamic stability of the three-dimensional axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional model that approximates the Navier-Stokes equations along the symmetry axis. An important property of this one-dimensional model is that one can construct from its solutions a family of exact solutions of the threedimensionaFin...

In [14], S. Montgomery-Smith provides a one dimensional model for the three dimensional, incompressible Navier-Stokes equations, for which he proves the blow up of solutions associated to a class of large initial data, while the same global existence results as for the Navier-Stokes equations hold for small data. In this note the model is adapted to the case of two and three space dimensions, w...

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 present finite volume schemes for Stokes and Navier-Stokes equations. These schemes are based on the mixed finite volume introduced in [6], and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier-Stokes equation...

We consider relativistic and ”semi-relativistic” models of radiative viscous compressible Navier-Stokes-Fourier system coupled to the radiative transfer equation extending the classical model introduced in [1] and we study some of its singular limits (low Mach and diffusion) in the case of well-prepared initial data and Dirichlet boundary condition for the velocity field. In the low Mach number...

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed ‘Non-linear grid system’ is presented. The linear terms in Navier-Stokes equation are solved by CrankNicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Split...

In this paper, we present first-, second-, and third-order implicit finite-volume schemes for solving the Navier-Stokes equations on unstructured grids based on a hyperbolic formulation of the viscous terms. These schemes are first-, second-, and third-order accurate on irregular grids for both the inviscid and viscous terms and for all Reynolds numbers, not only in the primitive variables but ...

The numerical implementation of a multilevel finite element method for the steadystate Navier–Stokes equations is considered. The multilevel method proposed here for the Navier– Stokes equations is a multiscale method in which the full nonlinear Navier–Stokes equations are only solved on a single coarse grid; subsequent approximations are generated on a succession of refined grids by solving a ...