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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TL;DR: Results for compressible gas-water systems show that the new method can simulate interface dynamics accurately, including the effect of surface tension, and can be used for simulations of fluid interface with large density differences.
244 citations
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TL;DR: In this article, an iterative method of Krylov subspace type is presented 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).
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.
244 citations
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TL;DR: In this paper, a linear stability analysis is presented for a wide variety of mixing layers, including low-speed and high-speed layers with variable density and high Mach number mixing layers.
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
244 citations
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TL;DR: In this paper, the authors derive analytic criteria for the existence of hyperbolic (attracting or repelling), elliptic, and parabolic material lines in 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.
244 citations
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TL;DR: A stabilized finite element approximation for the incompressible Navier–Stokes equations based on the subgrid-scale concept is analyzed and the properties of the discrete formulation that results allowing the sub grid-scales to depend on time are explored.
243 citations