We investigate the zero dissipation limit problem of the one dimensional compressible non–isentropic Navier–Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that the unique solution of the Navier–Stokes equations exists for all time, and converge to the Riemann solution of the corresponding Euler equations with the same Riemann initial...

I n the 1820s Claude Louis Marie Henri Navier1 was a professor at the École des Ponts et Chaussées in Paris, which was the Grande École that trained engineers in nineteenthcentury France. At the same time as publishing his famous fluid equations (now known as the Navier-Stokes equations), he designed the first monumental suspension bridge to be built in Paris over the Seine. His bridge develope...

Two-dimensional reactive Navier-Stokes equations are solved using a simple implicit Beam-Warming finite difference scheme. Comparisons of the detonation wave solutions of reactive Euler equations and reactive Navier-Stokes equations show that physical diffusion is important at high resolution when the numerical diffusion becomes negligible. Hence, for accurate detonation wave solutions it is ne...

A beautiful and influential subject in the study of the question of smoothness of solutions for the Navier – Stokes equations in three dimensions is the theory of partial regularity. A major paper on this topic is Caffarelli, Kohn & Nirenberg [5](1982) which gives an upper bound on the size of the singular set S(u) of a suitable weak solution u. In the present paper we describe a complementary ...

The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general (ill-prepared) initial data is rigorously proved in this paper. It is proved that, as the Debye length tends to zero, the solution of the compressible Navier-Stokes-Poisson system converges strongly to the strong solution of the incompressible Navier-Stokes equations plus a term of fast singul...

Towards direct simulations of counterflow flames with consistent differential-algebraic boundary conditions Report Title A new approach for the formulation of boundary conditions for the counterflow configuration is presented. Upon discretization of the steady-state Navier-Stokes equations at the inflow boundaries, numerically algebraic equations are imposed as boundary conditions, while upon d...

Abstract. We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in R with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the Navier boundary condition in terms of the vorticity, which is motivated by the Hodge theory on manifolds with boundary from the viewpoint of differential...

The direction splitting approach proposed earlier in [7], aiming at the efficient solution of Navier-Stokes equations, is extended and adopted here to solve the Navier-Stokes-Brinkman equations describing incompressible flows in pure fluid and in porous media. The resulting pressure equation is a perturbation of the incompressibility constraint using a direction-wise factorized operator as prop...