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 locally conservative LDG method for the incompressible Navier-Stokes equations

Abstract: In this paper a new local discontinuous Galerkin method for the incompressible stationary Navier-Stokes equations is proposed and analyzed. Four important features render this method unique: its stability, its local conservativity, its high-order accuracy, and the exact satisfaction of the incompressibility constraint. Although the method uses completely discontinuous approximations, a globally divergence-free approximate velocity in H(div; Ω) is obtained by simple, element-by-element post-processing. Optimal error estimates are proven and an iterative procedure used to compute the approximate solution is shown to converge. This procedure is nothing but a discrete version of the classical fixed point iteration used to obtain existence and uniqueness of solutions to the incompressible Navier-Stokes equations by solving a sequence of Oseen problems. Numerical results are shown which verify the theoretical rates of convergence. They also confirm the independence of the number of fixed point iterations with respect to the discretization parameters. Finally, they show that the method works well for a wide range of Reynolds numbers.

Simulating elliptic flow with viscous hydrodynamics

Abstract: In this work we simulate a viscous hydrodynamical model of noncentral Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance The model fluid equations were proposed by Oettinger and Grmela [Grmela, M, and Oettinger, H C, Phys Rev E, 56, 6620 (1997)] Freeze-out is signaled when the viscous corrections become large relative to the ideal terms Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest However, when these corrections are included, the elliptic flow is strongly modified at large p{sub T} We also investigate the stability of the viscous results by comparing the nonideal components of the stress tensor ({pi}{sup ij}) and their influence on the v{sub 2} spectrum to the expectation of the Navier-Stokes equations ({pi}{sup ij}=-{eta} ) We argue that when the stress tensor deviates from the Navier-Stokes form the dissipative corrections to spectra are too large for a hydrodynamic description to be reliable For typical Relativistic Heavy Ion Colloder initial conditions this happens for {eta}/s > or approx 03