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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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Journal ArticleDOI
TL;DR: A state-of-the-art method for solving the preconditioned compressible Navier–Stokes equations accurately and efficiently for a wide range of the Mach number with an immersed-boundary approach which allows one to use Cartesian grids for arbitrarily complex geometries is combined.

138 citations

Journal ArticleDOI
TL;DR: A cell-vertex scheme for the three-dimensional Navier-Stokes equations, which is based on central-difference approximations and Runge-Kutta time stepping, and the analysis of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios is described.
Abstract: A cell-vertex scheme for the three-dimensional Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing with locally varying coefficients, a multigrid method and carefully controlled dissipative terms, very good convergence rates are obtained for two- and three-dimensional flows. Details of the acceleration techniques, which are important for convergence on meshes with high aspect-ratio cells, are discussed. Emphasis is put on the analysis of the stability properties of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios.

138 citations

Journal ArticleDOI
TL;DR: An efficient self-adaptive strategy for the explicit time integration of Navier-Stokes equations is presented, which works independently of the underlying spatial mesh and can be easily integrated into structured or unstructured codes.
Abstract: An efficient self-adaptive strategy for the explicit time integration of Navier-Stokes equations is presented. Unlike the conventional explicit integration schemes, it is not based on a standard CFL condition. Instead, the eigenvalues of the dynamical system are analytically bounded and the linear stability domain of the time-integration scheme is adapted in order to maximize the time step. The method works independently of the underlying spatial mesh; therefore, it can be easily integrated into structured or unstructured codes. The additional computational cost is minimal, and a significant increase of the time step is achieved without losing accuracy. The effectiveness and robustness of the method are demonstrated on both a Cartesian staggered and an unstructured collocated formulation. In practice, CPU cost reductions up to more than 4 with respect to the conventional approach have been measured.

138 citations

Journal ArticleDOI
TL;DR: In this article, a direct numerical simulation of turbulent channel flow over a 3D Cartesian grid of cubes is performed, where the flow field is resolved with 600×400×400 mesh points.
Abstract: A direct numerical simulation (DNS) has been performed of turbulent channel flow over a three-dimensional Cartesian grid of 30×20×9 cubes in, respectively, the streamwise, spanwise, and wall-normal direction. The grid of cubes mimics a permeable wall with a porosity of 0.875. The flow field is resolved with 600×400×400 mesh points. To enforce the no-slip and no-penetration conditions on the cubes, an immersed boundary method is used. The results of the DNS are compared with a second DNS in which a continuum approach is used to model the flow through the grid of cubes. The continuum approach is based on the volume-averaged Navier–Stokes (VANS) equations [ S. Whitaker, “The Forchheimer equation: a theoretical development,” Transp. Porous Media 25, 27 (1996) ] for the volume-averaged flow field. This method has the advantage that it requires less computational power than the direct simulation of the flow through the grid of cubes. More in general, for complex porous media one is usually forced to use the VANS equations, because a direct simulation would not be possible with present-day computer facilities. A disadvantage of the continuum approach is that in order to solve the VANS equations, closures are needed for the drag force and the subfilter-scale stress. For porous media, the latter can often be neglected. In the present work, a relation for the drag force is adopted based on the Irmay [ “Modeles theoriques d’ecoulement dans les corps poreux,” Bulletin Rilem 29, 37 (1965) ] and the Burke–Plummer model [ R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (Wiley, New York, 2002) ], with the model coefficients determined from simulations reported by W. P. Breugem, B. J. Boersma, and R. E. Uittenbogaard [“Direct numerical simulation of plane channel flow over a 3D Cartesian grid of cubes,” Proceedings of the Second International Conference on Applications of Porous Media, edited by A. H. Reis and A. F. Miguel (Evora Geophysics Center, Evora, 2004), p. 27 ]. The results of the DNS with the grid of cubes and the second DNS in which the continuum approach is used, agree very well.

137 citations

Journal ArticleDOI
TL;DR: In this paper, the Navier-Stokes equations with Navier friction boundary conditions are considered and convergence to the expected limit system under a weaker hypothesis on the initial data is shown.
Abstract: We consider the Navier–Stokes equations with Navier friction boundary conditions and prove two results. First, in the case of a bounded domain we prove that weak Leray solutions converge (locally in time in dimension ≥3 and globally in time in dimension 2) as the viscosity goes to 0 to a strong solution of the Euler equations, provided that the initial data converge in L2 to a sufficiently smooth limit. Second, we consider the case of a half-space and anisotropic viscosities: we fix the horizontal viscosity, send the vertical viscosity to 0 and prove convergence to the expected limit system under a weaker hypothesis on the initial data.

137 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023183
2022389
2021544
2020509
2019545
2018575