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.

Variational bounds on energy dissipation in incompressible flows. III. Convection

Abstract: Building on a method of analysis for the Navier-Stokes equations introduced by Hopf [Math. Ann. 117, 764 (1941)], a variational principle for upper bounds on the largest possible time averaged convective heat flux is derived from the Boussinesq equations of motion. When supplied with appropriate test background fields satisfying a spectral constraint, reminiscent of an energy stability condition, the variational formulation produces rigorous upper bounds on the Nusselt number (Nu) as a function of the Rayleigh number (Ra). For the case of vertical heat convection between parallel plates in the absence of sidewalls, a simplified (but rigorous) formulation of the optimization problem yields the large Rayleigh number bound Nu\ensuremath{\le}0.167 ${\mathrm{Ra}}^{1/2}$-1. Nonlinear Euler-Lagrange equations for the optimal background fields are also derived, which allow us to make contact with the upper bound theory of Howard [J. Fluid Mech. 17, 405 (1963)] for statistically stationary flows. The structure of solutions of the Euler-Lagrange equations are elucidated from the geometry of the variational constraints, which sheds light on Busse's [J. Fluid Mech. 37, 457 (1969)] asymptotic analysis of general solutions to Howard's Euler-Lagrange equations. The results of our analysis are discussed in the context of theory, recent experiments, and direct numerical simulations. \textcopyright{} 1996 The American Physical Society.

Solution of the 2D Navier-Stokes equations on unstructured adaptive grids

Abstract: This paper presents a solution adaptive scheme for solving the Navier-Stokes equations on a n unstructured mixed grid of triangles and quadrilaterals. The solution procedure uses an explicit Itunge-Kutta finite volun~e time marching scheme. The solution is begun on a coarse grid and points are added adaptively during the solution procedure using criteria such as pressure and velocity gradients. In viscous regions the gradients are essentially one dimensional, and we use quadrilateral elements in these regions to facilitate the one dimensional refinement required for the efficient resolution of boundary layers and wakes. The effect of turbulence is modeled by the inclusion of a K E tubulence rnodel. When used for analyzing flows in turbomachinery blade rows, terms rrpresenting the effects of changes in strearnsheet lhicknrss and radius, and the effects of rotation are included. Axisymnletric flows with swirl can also be analyzed. Solutions are presented for several examples that illustrate the capability of the algorithm.

A vortex-based subgrid stress model for large-eddy simulation

Abstract: A class of subgrid stress (SGS) models for large-eddy simulation (LES) is presented based on the idea of structure-based Reynolds-stress closure. The subgrid structure of the turbulence is assumed to consist of stretched vortices whose orientations are determined by the resolved velocity field. An equation which relates the subgrid stress to the structure orientation and the subgrid kinetic energy, together with an assumed Kolmogorov energy spectrum for the subgrid vortices, gives a closed coupling of the SGS model dynamics to the filtered Navier-Stokes equations for the resolved flow quantities. The subgrid energy is calculated directly by use of a local balance between the total dissipation and the sum of the resolved-scale dissipation and production by the resolved scales. Simple one- and two-vortex models are proposed and tested in which the subgrid vortex orientations are either fixed by the local resolved velocity gradients, or rotate in response to the evolution of the gradient field. These models are not of the eddy viscosity type. LES calculations with the present models are described for 32^(3) decaying turbulence and also for forced 32^(3) box turbulence at Taylor Reynolds numbers R-lambda in the range R(lambda)similar or equal to 30 (fully resolved) to R-lambda=infinity. The models give good agreement with experiment for decaying turbulence and produce negligible SGS dissipation for forced turbulence in the limit of fully resolved flow.