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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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185 citations
TL;DR: In this paper, the Navier-Stokes equations on orthogonal grids are applied independently of the grid by assigning body forces over surfaces that need not coincide with coordinate lines.
Abstract: Anumericalmethodispresentedthatallowslargeeddysimulation (LES)ofturbulente owsincomplexgeometric cone gurations with moving boundaries and that retains the advantages of solving the Navier ‐Stokes equations on e xed orthogonal grids. The boundary conditions are applied independently of the grid by assigning body forces over surfaces that need not coincide with coordinate lines. The use of orthogonal, nondeforming grids simplie es grid generation, facilitates theimplementation of high-order,nondissipativediscretization schemes, andminimizes the spatial and temporal variations in e lter width that complicate unstructured deforming-grid LES. Dynamic subgrid-scaleturbulence models areparticularly appealing in combination with the body-forceprocedure because the dynamic model accounts automatically for the presence of solid walls without requiring damping functions. The method is validated by simulations of the turbulent e ow in a motored axisymmetric piston ‐cylinder assembly for which detailed experimental measurements are available. Computed mean and rms velocity proe les show very good agreement with measured ensemble averages. Thepresent numerical code runs on small, personal computerlike workstations. For a comparable level of accuracy, computational requirements (memory and CPU time ) are at least a factor of 10 lower compared to published simulations for the same cone guration obtained using an unstructured, boundary-e tted deforming-grid approach.
185 citations
TL;DR: A complete formulation using a modal basis which has been implemented in a new code NeκTαr of high order polynomial approximations on triangular domains as the next generation of spectral element solvers and a variety of results showing exponential convergence.
184 citations
TL;DR: The lower-upper symmetric Gauss-Seidel method is modified for the simulation of viscous flows on massively parallel computers, and a full matrix version of the DP-LUR method is derived.
Abstract: The lower-upper symmetric Gauss-Seidel method is modified for the simulation of viscous flows on massively parallel computers. The resulting diagonal data-parallel lower-upper relaxation (DP-LUR) method is shown to have good convergence properties on many problems. However, the convergence rate decreases on the high cell aspect ratio grids required to simulate high Reynolds number flows. Therefore, the diagonal approximation is relaxed, and a full matrix version of the DP-LUR method is derived. The full matrix method retains the data-parallel properties of the original and reduces the sensitivity of the convergence rate to the aspect ratio of the computational grid. Both methods are implemented on the Thinking Machines CM-5, and a large fraction of the peak theoretical performance of the machine is obtained. The low memory use and high parallel efficiency of the methods make them attractive for large-scale simulation of viscous flows.
184 citations
TL;DR: In this article, the Navier-Stokes equations of a viscous incompresible fluid were considered and the authors showed that the solutions are entirely determined by their values on a discrete set, provided this set contains enough points and these points are sufficiently densely distributed.
Abstract: We consider the Navier-Stokes equations of a viscous incompresible fluid, and we want to see to what extent these solutions can be determined by a discrete set of nodal values of these solutions. The results presented here are exact results and not approximate ones: we show, in several cases, that the solutions are entirely determined by their values on a discrete set, provided this set contains enough points and these points are sufficiently densely distributed (in a sense described in the article). Two typical results are the following ones; two stationary solutions coincide if they coincide on a set sufficiently dense but finite; similarly if the large time behavior of the solutions to the Navier-Stokes equations is known on an appropriate discrete set, then the large time behavior of the solution itself is totally determined.
184 citations