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: In this paper, various methods of linking the Navier-stokes and the Darcy equations in a solution scheme are considered and the strength and weaknesses of these methods are discussed.
136 citations
TL;DR: The stochastically forced, two-dimensional, incompressable Navier–Stokes equations are shown to possess an unique invariant measure if the viscosity is taken large enough, which follows from a stronger result showing that at high viscolysis there is a unique stationary solution which attracts solutions started from arbitrary initial conditions.
Abstract: The stochastically forced, two-dimensional, incompressable Navier–Stokes equations are shown to possess an unique invariant measure if the viscosity is taken large enough. This result follows from a stronger result showing that at high viscosity there is a unique stationary solution which attracts solutions started from arbitrary initial conditions. That is to say, the system has a trivial random attractor. Along the way, results controling the expectation and averaging time of the energy and enstrophy are given.
136 citations
TL;DR: Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number of 20,000 with fourth order spatial accuracy.
Abstract: SUMMARY A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes equations can easily be applied to this fourth order compact formulation. In particular in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601×601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number of 20,000 with fourth order spatial accuracy. Detailed solutions are presented.
136 citations
TL;DR: In this article, a 2D particle-based model for the red blood cell is presented, where the cell membrane is replaced by a set of discrete particles connected by nonlinear springs.
136 citations
TL;DR: In this paper, a multiscale finite element method for the incompressible Navier-Stokes equations is proposed, which is based on a decomposition of the velocity field into coarse/resolved scales and fine/unsolved scales.
136 citations