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.

Dynamic One-Equation Nonviscosity Large-Eddy Simulation Model

Abstract: Anew approach for a nonviscosity large-eddy simulation (LES)subgrid stress model is presented.Theapproach uses a scaling that is provided by the subgrid kinetic energy and a tensor coefe cient that is obtained from the dynamic modeling approach, hence, a dynamic structure model. Mathematical and conceptual issues motivating the development of this new model are explored. Attention is focused on dynamic modeling approaches. The basic equations that originate in dynamic modeling approaches are Fredholm integral equations of the second kind. These equations have solvability requirements that have not been previously addressed in the context of LES models. These conditionsare examined for traditional dynamic Smagorinksy modeling, that is, zero-equation approaches, and one-equation subgrid models. It is shown that standard approaches do not always satisfy the integral equation solvability condition. It is also shown that traditional LES models that use the resolved scale strain rate to estimatethesubgrid stressesscalepoorly with e lterlevel, leading to signie cant errorsin themodeling of the subgrid scale stress. The poor scaling in traditional LES approaches can result in not only weak models, but can also cause nonrealizability of the subgrid stresses. A better scaling based on the subgrid kinetic energy is proposed that leads to a new one-equation nonviscosity model that does satisfy the solvability conditions and appears to maintain realizability. Both integral and algebraic formulations of the new one-equation nonviscosity model are presented. The resolved and subgrid kinetic energies are shown to compare well to a direct numerical simulation of decaying isotropic turbulence.

Solutions of the Navier-Stokes equations for vortex breakdown

Abstract: Steady solutions of the Navier-Stokes equations, in terms of velocity and pressure, for breakdown in an unconfined viscous vortex are obtained numerically using the artificial compressibility technique of Chorin combined with an ADI finite-difference scheme. Axisymmetry is assumed and boundary conditions are carefully applied at the boundaries of a large finite region in an axial plane while resolution near the axis is maintained by a coordinate transformation. The solutions, which are obtained for Reynolds numbers up to 200 based on the free-stream axial velocity and a characteristic core radius, show that breakdown results from the diffusion and convection of vorticity away from the vortex core which, because of the strong coupling between the circumferential and axial velocity fields in strongly swirling flows, can lead to stagnation and reversal of the axial flow near the axis.

Effective eddy viscosities in implicit large eddy simulations of turbulent flows

Abstract: We propose a method for computing effective numerical eddy viscosity acting in dissipative numerical schemes used in monotonically integrated large eddy simulations of turbulence. The method is evaluated on an example of a specific nonoscillatory finite volume scheme MPDATA developed for simulations of geophysical flows.

Modelling of bypass transition with conditioned Navier-Stokes equations coupled to an intermittency transport equation

Abstract: A differential method is proposed to simulate bypass transition. The intermittency in the transition zone is taken into account by conditioned averages. These are averages taken during the fraction of time the flow is turbulent or laminar respectively. Starting from the Navier-Stokes equations, conditioned continuity, momentum and energy equations are derived for the larninar and turbulent parts of the intermittent flow. The turbulence is described by a classical k-e model. The supplementary parameter, the intermittency factor, is determined by a transport equation applicable for zero, favourable and adverse pressure gradients. Results for these pressure gradients are given.