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.

A Preconditioner for the Steady-State Navier--Stokes Equations

Abstract: We present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady-state Navier--Stokes equations (also known as the Oseen equations). The solver is an iterative method of Krylov subspace type for which we devise a preconditioner through a heuristic argument based on the fundamental solution tensor for the Oseen operator. The preconditioner may also be conceived through a weaker heuristic argument involving differential operators. Computations indicate that convergence for the preconditioned discrete Oseen problem is only mildly dependent on the viscosity (inverse Reynolds number) and, most importantly, that the number of iterations does not grow as the mesh size is reduced. Indeed, since the preconditioner is motivated through analysis of continuous operators, the number of iterations decreases for smaller mesh size which accords with better approximation of these operators.

Compressible mixing layer - Linear theory and direct simulation

Abstract: Results from linear stability analysis are presented for a wide variety of mixing layers, including low-speed layers with variable density and high Mach number mixing layers. The linear amplification predicts correctly the experimentally observed trends in growth rate that are due to velocity ratio, density ratio, and Mach number, provided that the spatial theory is used and the mean flow is a computed solution of the compressible boundary-layer equations. It is found that three-dimensional modes are dominant in the high-speed mixing layer above a convective Mach number of 0.6, and a simple relationship is proposed that approximately describes the orientation of these waves. Direct numerical simulations of the compressible Navier-Stokes equations are used to show the reduced growth rate that is due to increasing Mach number. From consideration of the compressible vorticity equation, it is found that the dominant physics controlling the nonlinear roll-up of vortices in the high-speed mixing layer is contained in an elementary form in the linear eigenfunctions. It is concluded that the linear theory can be very useful for investigating the physics of free shear layers and predicting the growth rate of the developed plane mixing layer

Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence

Abstract: We derive analytic criteria for the existence of hyperbolic (attracting or repelling), elliptic, and parabolic material lines in two-dimensional turbulence. The criteria use a frame-independent Eulerian partition of the physical space that is based on the sign definiteness of the strain acceleration tensor over directions of zero strain. For Navier–Stokes flows, our hyperbolicity criterion can be reformulated in terms of strain, vorticity, pressure, viscous and body forces. The special material lines we identify allow us to locate different kinds of material structures that enhance or suppress finite-time turbulent mixing: stretching and folding lines, Lagrangian vortex cores, and shear jets. We illustrate the use of our criteria on simulations of two-dimensional barotropic turbulence.