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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Solution algorithms for pressure-velocity coupling in steady flows ： ウィキペディア英語版 Solution algorithms for pressure-velocity coupling in steady flows Solution algorithms for pressure-velocity coupling in steady flows are the standard prepossessing methods used to solve steady problems in computational fluid dynamics. The advection of the scalar Φ used to define flow depends on the magnitude and direction of the local velocity field. In general, however the velocity field is not known. These algorithms are hence employed to obtain the solution. The standard Euler equations (fluid dynamics) can be given by: The continuity equation : $\backslash frac\; +\; \backslash frac\; =\; 0$ The momentum equations Obtained by substituting Φ with standard directional vectors of the velocity field ''u'', ''v'', and ''w''. : $\backslash frac\; +\; \backslash frac\; =\; \backslash frac\}\; +\; \backslash frac\}\; -\; \backslash frac\; +\; S\_u$ : $\backslash frac\; +\; \backslash frac\; =\; \backslash frac\}\; +\; \backslash frac\}\; -\; \backslash frac\; +\; S\_v$ where $\backslash rho$ is the density, ''u'', ''v'', are the ''x''- and ''y''-directional components of velocity, ''p'' is the pressure field and ''S''''u'',''v'' are the source terms. These equations are however hard to solve due to quasilinearity in the momentum equations and interdependence of the pressure term in all three equations. Also, for a general purpose flow equation, the pressure field is also unknown and is to be solved for as well. If the flow field is compressible, the above equations act as the standard temperature and density equations and pressure can be found as it is a function of them both. If, however the flow is in-compressible, the pressure is independent of density. Hence, coupling is necessary to induce a constraint on the solution. The resulting fields will then satisfy the continuity equations. Both these issues are solved via the application of the SIMPLE Algorithm and its derivatives. For general purpose and definition of these algorithms, a Staggered CFD Grid shall be used. It ensures the presence of very real non-zero pressure gradient across the nodes in any condition, even in the case of a checkered grid. The staggering also ensures realistic behaviors of the descretized momentum equations for spatially oscillating pressures. Also, the direction of the velocity vectors are exact. == The staggered grid == Standard staggered grid in computational fluid dynamics The above shows a standard grid used to solve staggered applications. The east, west, north and south notations are used. They direct the vector fields. The u component of velocity is stored in the e and w directions and the v component in the n and s directions. If 3-D fields are to applied, t and b can be used. These are basically vector control volumes different from the scalar pressure control volumes and different from each other. The pressure gradient equations take a different form: : $\backslash frac\; =\; \backslash frac$ in the ''x''-direction : $\backslash frac\; =\; \backslash frac$ in the ''y''-direction Furthermore, the momentum equations now take the form: : $a\_i,\_J\; u\_i,\_J\; =\; \backslash sum\; a\_nb\; u\_nb\; -\; \backslash Delta\; V\_u\; \backslash frac\; +\; S\; \backslash Delta\; V\_u$ The summation covers all nodes and volumes in the immediate vicinity of the selected node. Their values are shown in the next figure. Refined segregated Grid Following this, The algorithms can be applied to get the solutions for the basic staggered grid equations. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Solution algorithms for pressure-velocity coupling in steady flows」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.