We consider an unbiased approximation of stochastic Navier-Stokes equation driven by spatial white noise. This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier-Stokes equation. The nonlinear term can be characterized as the highest stochastic order approximation of the original nonlinear term u∇u. We investigate the analyti...

In the paper compressible, stationary Navier-Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions, i.e., the solutions take form (1.12). The approximate soluti...

this work reports the results of the application of the second-order maccormack method for numerical solution of‎ the conservative form of two-dimensional non-hydrostatic and fully compressible navier-stokes equations governing an inviscid and adiabatic atmosphere‎. various aspects of the computational approach such as discretization of the governing equations for the interior and boundary poin...

In this article, a non linear family of spaces, based on the energy dissipation, is introduced. This family bridges an energy space (containing weak solutions to Navier-Stokes equation) to a critical space (invariant through the canonical scaling of the Navier-Stokes equation). This family is used to get uniform estimates on higher derivatives to solutions to the 3D Navier-Stokes equations. Tho...

In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantl...

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...

Both the particle based Direct Simulation Monte Carlo (DSMC) method and a compressible Navier-Stokes based continuum method are used to investigate the flow inside micronozzles and to predict the performance of such devices. For the Navier-Stokes approach, both slip and no-slip boundary conditions are applied. Moreover, the two methods have been coupled to be used together in a hybrid particle-...

In this work, the Characteristic-Based-Split (CBS) scheme is combined with the Minimum Polynomial Extrapolation (MPE) method to solve Navier-Stokes problems. We show the case of natural convection where the Navier--Stokes equations are coupled with the temperature equation. The local temperature difference induces a local density difference within the fluid and this produce the fluid motion. BU...

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations with degenerate viscosity, and a nonlinear third-order differential operator, with the quantum Bohm potential, and the damping terms. The global weak solution...