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 work, we obtain the hydrostatic approximation by taking small aspect ratio limit to Navier–Stokes equations. The (the of depth horizontal width) is a geometrical constraint in general large scale motions meaning that vertical significantly smaller than horizontal. We use versatile relative entropy inequality prove rigorously from compressible equations Primitive Equations. This first wo...

We consider a heat conducting compressible viscous fluid at rest in a rigid container and show that the thermal and the kinetic energy of arbitrary disturbances of the rest state eventually decays. REsuME. On considere un fluide compressible, visqueux et conducteur de la chaleur au repos dans un reservoir rigide. On montre que l'energie thermique et cinetique de perturbations arbitraires est am...

The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock...

The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock...

This paper is concerned with the self-similar solutions to the compressible Navier-Stokes equations of a 1D viscous polytropic ideal gas. Our results show that there exist neither forward nor backward selfsimilar solutions with finite total energy, which generalizes the results for the case of the isothermal compressible Navier-Stokes equations in Z. Guo and S. Jiang (Self-similar solutions to ...

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...

A characteristic-based semi-Lagrangian (CSL) method is developed for hyperbolic systems of conservation laws. In the CSL method, the governing equations are first transformed into a system of equations in characteristic form and then the Lagrangian form of the transformed equations is solved along the characteristic directions. By definition of hyperbolicity, such a transformation always exists...

This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier–Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers’s equa...

The objective in this paper is to present some developments for the analysis of Navier–Stokes incompressible and compressible fluid flows with structural interactions. The incompressible fluid is discretized with a new solution approach, a flow-condition-based interpolation finite element scheme. The high-speed compressible fluids are solved using standard finite volume methods. The fluids are ...