Compressible Navier–Stokes models for quantum fluids are reviewed. They are derived from a collisional Wigner equation by a moment method and a Chapman–Enskog expansion around the quantum equilibrium. Introducing a new velocity variable, the barotropic quantum Navier-Stokes model can be reformulated as a viscous quantum Euler system, which possesses a new Lyapunov (energy) functional. This func...

A method based on the simple shear flow modified by the introduction of a deterministic non-conservative force and a stochastic process is proposed to measure the Navier–Stokes shear viscosity in a granular fluid described by the Enskog equation. The method is implemented in DSMC simulations for a wide range of values of dissipation and density. It is observed that, after a certain transient pe...

The volume penalty method provides a simple, efficient approach for solving the incompressible Navier-Stokes equations in domains with boundaries or in the presence of moving objects. Despite the simplicity, the method suffers from poor convergence in the penalty parameter, thereby restricting accuracy of any numerical method. We demonstrate that one may achieve high order accuracy by introduci...

The kinetic theory for a fluid of hard spheres which undergo endothermic and/or exothermic reactions with mass transfer is developed. The exact balance equations for concentration, density, velocity, and temperature are derived. The Enskog approximation is discussed and used as the basis for the derivation, via the Chapman-Enskog procedure, of the Navier-Stokes reaction equations under various ...

We consider cascade models of turbulence which are obtained by restricting the Navier-Stokes equation to local interactions. By combining the results of the method of extended self-similarity and a novel subgrid model, we investigate the inertial range fluctuations of the cascade. Significant corrections to the classical scaling exponents are found. The dynamics of our local Navier-Stokes model...

We present a nonlinear model predictive framework for closedloop control of two-phase flows governed by the Cahn-Hilliard NavierStokes system. We adapt the concept for instantaneous control from [6, 12, 16] to construct distributed closed-loop control strategies for twophase flows. It is well known that distributed instantaneous control is able to stabilize the Burger’s equation [16] and also t...

In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible fluid in a bounded domain of the plane. The first system corresponds to an inviscid fluid driven by the Euler equation whereas the other one corresponds to a viscous fluid driven by the Navier-Stokes system. In both cases we investigate the uniqueness of weak solutions, à la Yudovich for the Eule...

We introduce a method of estimating the space analyticity radius of solutions for the Navier Stokes and related equations in terms of L p and L norms of the initial data. The method enables us to express the space analyticity radius for 3D Navier Stokes equations in terms of the Reynolds number of the flow. Also, for the Kuramoto Sivashinsky equation, we give a partial answer to a conjecture th...

Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Ch...

We consider the inviscid limit of the stochastic damped 2D NavierStokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier-Stokes equations converges to a stationary solution of the stochastic damped Euler equation and that the rate of dissipation of enstrophy converges to zero. In particular, this limit obeys an enstrophy balance. The...