The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an ocial endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and Space Administration. Summary Two computational methods are used to predict the ow over a generic helicopter fuselage of a simple conguration. A thin-layer Navier-Stok...

Upwind schemes for the Euler and Navier-Stokes equations may be broadly classified into two distinct classes: those based directly on the macroscopic Navier-Stokes equations and those based indirectly on the Navier-Stokes equations via the Boltzmann equation. The former, conventional approach represents the majority of current research. However, recently gas-kinetic methods have gained attentio...

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 study in this article both the structure and the structural evolution of the solutions of 2-D Navier-Stokes equations with periodic boundary conditions and the evolution of their solutions. First the structure of all eigenvectors of the corresponding Stokes problem is classified using a block structure, and is linked to the typical structure of the Taylor vortices. Then the structure of the ...

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...

This article describes a new numerical solver for the Navier-Stokes equations. The proposed solver is written in Python which is a newly developed language. The Python packages are built to solve the Navier-Stokes equations with existing libraries. We have created discretized coefficient matrices from systems of the Navier-Stokes equations by the finite difference method. In addition we focus o...

A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations. The time discretization of the penalty Navier-Stokes equations is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Navier-Stokes equations is based on a finite element space pair (Xh,Mh) which satisfies some approximate assumpt...

We investigate the self-similar solutions to the isothermal compressible Navier–Stokes equations. The aim of this paper is to show that there exist neither forward nor backward self-similar solutions with finite total energy. This generalizes the results for the incompressible case in Nečas, J., Ru̇žička, M. & Šverák, V. (1996, On Leray’s self-similar solutions of the Navier-Stokes equations. Ac...

We consider two-grid mixed-finite element schemes for the spatial discretization of the incompressible Navier-Stokes equations. A standard mixed-finite element method is applied over the coarse grid to approximate the nonlinear Navier-Stokes equations while a linear evolutionary problem is solved over the fine grid. The previously computed Galerkin approximation to the velocity is used to linea...

The integrals arising from potentials for two-dimensional Stokes equations are explored in the case when the potentials are defined on the smooth open arc of an arbitrary shape, while the densities in the potentials belong to weighted Hölder space and may have power singularities. The properties of smoothness of these integrals and their derivatives are studied. The singularities of the derivat...