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.

Finite element discretization of the Navier–Stokes equations with a free capillary surface

Abstract: The instationary Navier–Stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions. A stable finite element discretization is presented. The key idea is the treatment of the curvature terms by a variational formulation. In the context of a discontinuous in time space–time element discretization stability in (weak) energy norms can be proved. Numerical examples in 2 and 3 space dimensions are given.

Beyond Navier–Stokes: Burnett equations for flows in the continuum–transition regime

Abstract: In hypersonic flows about space vehicles in low earth orbits or flows in microchannels of microelectromechanical devices, the local Knudsen number lies in the continuum–transition regime Navier–Stokes equations are not adequate to model these flows since they are based on small deviation from local thermodynamic equilibrium To model these flows, a number of extended hydrodynamics or generalized hydrodynamics models have been proposed over the past fifty years, along with the direct simulation Monte Carlo (DSMC) approach One of these models is the Burnett equations which are obtained from the Chapman–Enskog expansion of the Boltzmann equation [with Knudsen number (Kn) as a small parameter] to O(Kn2) With the currently available computing power, it has been possible in recent years to numerically solve the Burnett equations However, attempts at solving the Burnett equations have uncovered many physical and numerical difficulties with the Burnett model As a result, several improvements to the conventio

The Numerical Solution of the Navier-Stokes Equations for an Incompressible Fluid

Abstract: A finite difference method for solving the Navier-Stokes equations for an incompressible fluid has been developed. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Essentially it constitutes an extension to time dependent problems of the artificial compressibility method introduced in [ l ] for steady flow problems. The equations to be solved can be written in the dimensionless form

Direct optimal growth analysis for timesteppers

Abstract: Methods are described for transient growth analysis of flows with arbitrary geometric complexity, where in particular the flow is not required to vary slowly in the streamwise direction. Emphasis is on capturing the global effects arising from localized convective stability in streamwise-varying flows. The methods employ the 'timestepper's approach' in which a nonlinear Navier-Stokes code is modified to provide evolution operators for both the forward and adjoint linearized equations. First, the underlying mathematical treatment in primitive flow variables is presented. Then, details are given for the inner level code modifications and outer level eigenvalue and SVD algorithms in the timestepper's approach. Finally, some examples are shown and guidance provided on practical aspects of this type of large-scale stability analysis. Copyright (C) 2008 John Wiley & Sons, Ltd.