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, an LES-type variational multiscale theory of turbulence is presented, which derives completely from the incompressible Navier-Stokes equations and does not employ any ad hoc devices such as eddy viscosities.
967 citations
01 Aug 2001
TL;DR: The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer graphics applications.
Abstract: In this paper, we propose a new approach to numerical smoke simulation for computer graphics applications. The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer graphics applications (as compared to the much finer grids used in the computational fluid dynamics literature). We use the inviscid Euler equations in our model, since they are usually more appropriate for gas modeling and less computationally intensive than the viscous Navier-Stokes equations used by others. In addition, we introduce a physically consistent vorticity confinement term to model the small scale rolling features characteristic of smoke that are absent on most coarse grid simulations. Our model also correctly handles the inter-action of smoke with moving objects.
937 citations
TL;DR: A time-derivative preconditioning of the Navier-Stokes equations, suitable for both variable and constant density fluids, is developed and is shown to provide accurate steady-state solutions for transonic and low-speed flow of variable density fluids.
Abstract: A time-derivative preconditioning of the Navier-Stokes equations, suitable for both variable and constant density fluids, is developed. The ideas of low-Mach-number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density-based, time-marching schemes for solving flows of incompressible and variable density fluids at all speeds. The preconditioning is coupled with a dual time-stepping scheme implemented within an explicit, multistage algorithm for solving time-accurate flows. The resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured, solution-adaptive mesh topologies. This method is shown to provide accurate steady-state solutions for transonic and low-speed flow of variable density fluids. The time-accurate solution of unsteady, incompressible flow is also demonstrated.
925 citations
TL;DR: The resulting discrete Boltzmann models are based on a kinetic representation of the fluid dynamics, hence the drawbacks in conventional higher-order hydrodynamic formulations can be avoided.
Abstract: We present in detail a theoretical framework for representing hydrodynamic systems through a systematic discretization of the Boltzmann kinetic equation. The work is an extension of a previously proposed formulation. Conventional lattice Boltzmann models can be shown to be directly derivable from this systematic approach. Furthermore, we provide here a clear and rigorous procedure for obtaining higher-order approximations to the continuum Boltzmann equation. The resulting macroscopic moment equations at each level of the systematic discretization give rise to the Navier–Stokes hydrodynamics and those beyond. In addition, theoretical indications to the order of accuracy requirements are given for each discrete approximation, for thermohydrodynamic systems, and for fluid systems involving long-range interactions. All these are important for complex and micro-scale flows and are missing in the conventional Navier–Stokes order descriptions. The resulting discrete Boltzmann models are based on a kinetic representation of the fluid dynamics, hence the drawbacks in conventional higher-order hydrodynamic formulations can be avoided.
914 citations
TL;DR: The data-parallel line relaxation method combines the fast convergence of the Gauss ‐Seidel line Relaxation method with a high parallel efe ciency and thus shows promise for large-scale simulation of viscous e ows.
Abstract: The Gauss‐Seidel line relaxation method is modie ed for the simulation of viscous e ows on massively parallel computers. The resulting data-parallel line relaxation method is shown to have good convergence properties for a seriesoftestcases.Thenewmethodrequiressignie cantlymorememorythanthepreviouslydevelopeddata-parallel relaxation methods, but it reaches a steady-state solution in much less time for all cases tested to date. In addition, the data-parallel line relaxation method shows good convergence properties even on the high-cell-aspect-ratio grids required to simulate high-Reynolds-number e ows. The new method is implemented using message passing on the Cray T3E, and the parallel performance of the method on this machine is discussed. The data-parallel line relaxation method combines the fast convergence of the Gauss ‐Seidel line relaxation method with a high parallel efe ciency and thus shows promise for large-scale simulation of viscous e ows.
874 citations