Navier–Stokes equations

About: Navier–Stokes equations is a research topic. Over the lifetime, 18180 publications have been published within this topic receiving 552555 citations. The topic is also known as: Navier-Stokes equations.

Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes I. Abstract framework, a volume distribution of holes

Abstract: This paper treats the homogenization of the Stokes or Navier-Stokes equations with a Dirichlet boundary condition in a domain containing many tiny solid obstacles, periodically distributed in each direction of the axes. (For example, in the three-dimensional case, the obstacles have a size of e3 and are located at the nodes of a regular mesh of size e.) A suitable extension of the pressure is used to prove the convergence of the homogenization process to a Brinkman-type law (in which a linear zero-order term for the velocity is added to a Stokes or Navier-Stokes equation).

Decay of Dissipative Equations and Negative Sobolev Spaces

Abstract: We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible Navier-Stokes equations and the Boltzmann equation. In particular, the optimal decay rates of the higher-order spatial derivatives of solutions are obtained. The negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

Abstract: The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

A Detailed Analysis of Film–Cooling Physics: Part I — Streamwise Injection With Cylindrical Holes

Abstract: A previously documented systematic computational methodology is implemented and applied to a jet-in-crossflow problem in order to document all of the pertinent flow physics associated with a film-cooling flowfield Numerical results are compared to experimental data for the case of a row of three-dimensional, inclined jets with length-to-diameter ratios similar to a realistic film-cooling application A novel vorticity-based approach is included in the analysis of the flow physics Particular attention has been paid to the downstream coolant structures and to the source and influence of counterrotating vortices in the crossflow region It is shown that the vorticity in the boundary layers within the film hole is primarily responsible for this secondary motion Important aspects of the study include: (1) a systematic treatment of the key numerical issues, including accurate computational modeling of the physical problem, exact geometry and high-quality grid generation techniques, higher-order numerical discretization, and accurate evaluation of turbulence model performance; (2) vorticity-based analysis and documentation of the physical mechanisms of jet-crossflow interaction and their influence on film-cooling performance; (3) a comparison of computational results to experimental data; and (4) comparison of results using a two-layer model near-wall treatment versus generalized wall functions Solution of the steady, time-averaged Navier-Stokes equations were obtained for all cases using an unstructured/adaptive grid, fully explicit, time-marching code with multigrid, local time stepping, and residual smoothing acceleration techniques For the case using the two-layer model, the solution was obtained with an implicit, pressure-correction solver with multigrid The three-dimensional test case was examined for two different film-hole length-to-diameter ratios of 175 and 35, and three different blowing ratios, from 05 to 20 All of the simulations had a density ratio of 20, and an injection angle of 35 deg An improved understanding of the flow physics has provided insight into future advances to film-cooling configuration design In addition, the advantages and disadvantages of the two-layer turbulence model are highlighted for this class of problems

Vacuum states for compressible flow

Abstract: In this paper we study the evolutions of the interfaces between gases and the vacuum for both inviscid and viscous one dimensional isentropic gas motions. The local (in time) existence of solutions for both inviscid and viscous models with initial data containing vacuum states is proved and some singular properties on the free surfaces separating the gas and the vacuum are obtained. It is found that the Euler equations are better behaved near the vacuum than the compressible Navier-Stokes equations. The Navier-Stokes equations with viscosity depending on density are introduced, which is shown to be well-posed (at least locally) and yield the desired solutions near vacuum.