We consider dynamics system with damping, which are obtained by some transformations from the system of incompressible Navier-Stokes equations. These have similar properties to original Navier-Stokes equations the scaling invariance. Due to the presence of the damping term, conclusions are different with proving the origin of the incompressible Navier-Stokes equations and get some new conclusio...

This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of ...

4 Phenomenologi al Equation Closure. 7 4 1 Examples 8 Example: River Flow 8 Quasi-equilibrium approximation 8 Example: TraÆ Flow 9 Example: Heat Condu tion 10 Fi k's Law 10 Thermal ondu tivity, difusivity, heat equation 10 Example: Granular Flow 11 Example: Invis id Fluid Flow 12 In ompressible Euler Equations 12 In ompressible Navier-Stokes Equations 12 Gas Dynami s 13 Equation of State 13 Ise...

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...

We propose a novel second order in time numerical scheme for Cahn-Hilliard-NavierStokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation. We show that the scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, ...

We derive a posteriori estimates for the modeling error caused by the assumption of perfect incompressibility in the incompressible NavierStokes equation: Real fluids are never perfectly incompressible, but always feature at least some low amount of compressibility. Thus, their behavior is described by the compressible Navier-Stokes equation, the pressure being a steep function of the density. ...

Conjugate heat transfer problems are of importance in many engineering applications, since flows are usually confined by some material with heat transfer properties. Whenever there is a temperature difference between the fluid and solid, heat will be transfered and change the flow properties in a non-trivial way (Giles 1997; Henshaw & Chand 2009; Lindström & Nordström 2010; Roe et al. 2008). Th...

in the present study, the nonlinear model of non-newtonian blood flow in cosine-shape stenosed elastic artery is numerically examined. the model is carried out for axisymmetric, two-dimensional and fully developed blood flow. the vessel wall is assumed to be have time-dependent radius that is important factor for study of blood flow. the cosine-shape stenosis convert to rigid artery by using a ...

Abstract. In this paper we prove a local exact controllability of the Navier–Stokes equations with the condition on the pressure on parts of the boundary. The local exact controllability is proved by using a global Carleman inequality and an estimate of an equation adjoint to a linearized Navier– Stokes equation with the nonstandard boundary condition. We also obtain the null controllability of...

We recover the Navier-Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a meso-scopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier-Stokes equation in a fixed time interval. The proof does not use non-gradient methods or the multi-scale analysis due to the long range jumps.