Topic
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.
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01 Jan 1975
TL;DR: In this article, a numerical method for solving the compressible form of the unsteady Navier-Stokes equations is described, with emphasis on the choice of a computational mesh for high Reynolds number flows, finitedifference approximations for mixed partial derivatives, extension of the Courant-Friedrichs-Lewy stability condition for viscous flows, mesh boundary conditions, and numerical smoothing for strong shock-wave calculations.
Abstract: A numerical method for solving the compressible form of the unsteady Navier-Stokes equations is described. This method was originally presented in 1970 and has since been modified during the development of computer programs at Ames for implementing models that account for the effects of turbulence in shock-induced separated flows. Although this paper does not describe the turbulence models themselves, a complete description of the basic numerical method is given with emphasis on the choice of a computational mesh for high Reynolds number flows, finite-difference approximations for mixed partial derivatives, extension of the Courant-Friedrichs-Lewy stability condition for viscous flows, mesh boundary conditions, and numerical smoothing for strong shock-wave calculations.
252 citations
TL;DR: In this article, a fictitious domain method for the numerical solutions of three-dimensional elliptic problems with Dirichlet boundary conditions and also of the Navier-Stokes equations modeling incompressible viscous flow was discussed.
251 citations
TL;DR: In this article, it was shown that the weak Navier-Stokes equations on any bounded, smooth three-dimensional domain have a global attractor for any positive value of the viscosity.
Abstract: In this paper we show that the weak solutions of the Navier-Stokes equations on any bounded, smooth three-dimensional domain have a global attractor for any positive value of the viscosity. The proof of this result, which bypasses the two issues of the possible nonuniqueness of the weak solutions and the possible lack of global regularity of the strong solutions, is based on a new point of view for the construction of the semiflow generated by these equations. We also show that, under added assumptions, this global attractor consists entirely of strong solutions.
250 citations
TL;DR: In this article, the authors studied the low Mach number limit for the Navier-Stokes equations and proved that solutions exist and they are uniformly bounded for a time interval which is independent of the Mach number Ma ∈ (0,1), the Reynolds number Re ∈ [1,+∞] and the Peclet number Pe ∈
Abstract: The low Mach number limit for classical solutions of the full Navier-Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are taken into account. In particular, we consider general initial data. The equations lead to a singular problem, depending on a small scaling parameter, whose linearized system is not uniformly well-posed. Yet, it is proved that solutions exist and they are uniformly bounded for a time interval which is independent of the Mach number Ma ∈ (0,1], the Reynolds number Re ∈ [1,+∞] and the Peclet number Pe ∈ [1,+∞]. Based on uniform estimates in Sobolev spaces, and using a theorem of G. Metivier & S. Schochet [30], we next prove that the penalized terms converge strongly to zero. This allows us to rigorously justify, at least in the whole space case, the well-known computations given in the introduction of P.-L. Lions' book [26].
249 citations
TL;DR: In this paper, the fluid flow outside of a stretching cylinder is studied, governed by a third-order nonlinear ordinary differential equation that leads to exact similarity solutions of the Navier-Stokes equations.
Abstract: The fluid flow outside of a stretching cylinder is studied. The problem is governed by a third‐order nonlinear ordinary differential equation that leads to exact similarity solutions of the Navier–Stokes equations. Because of algebraic decay, an exponential transform is used to facilitate numerical integration. Asymptotic solutions for large Reynolds numbers compare well with numerical results. The heat transfer is determined.
248 citations