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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 Finite volume method for unsteady flow ： ウィキペディア英語版 Finite volume method for unsteady flow Unsteady flows are characterized as flows in which the properties of the fluid are time dependent. It gets reflected in the governing equations as the time derivative of the properties are absent. For Studying Finite-volume method for unsteady flow there is some governing equations 〔http://books.google.co.in/books+finite+volume+method+for+unsteady+flows〕> ==Governing Equation== The conservation equation for the transport of a scalar in unsteady flow has the general form as 〔An Introduction to Computational Fluid Dynamics H. K. Versteeg and W Malalasekra Chapter 8 page 168〕 $\backslash frac\; +\; \backslash operatorname(\backslash rho\; \backslash phi\; \backslash upsilon)\; =\; \backslash operatorname(\backslash Gamma\; \backslash operatorname\; \backslash phi)\; +\; S\_\backslash phi$ $\backslash rho$ is density and $\backslash phi$ is conservative form of all fluid flow, $\backslash Gamma$ is the Diffusion coefficient and $S$ is the Source term. $\backslash operatorname(\backslash rho\; \backslash phi\; \backslash upsilon)$ is Net rate of flow of $\backslash phi$ out of fluid element(convection), $\backslash operatorname(\backslash Gamma\; \backslash operatorname\; \backslash phi)$ is Rate of increase of $\backslash phi$ due to diffusion, $S\_\backslash phi$ is Rate of increase of $\backslash phi$ due to sources. $\backslash frac$ is Rate of increase of $\backslash phi$ of fluid element(transient), The first term of the equation reflects the unsteadiness of the flow and is absent in case of steady flows. The finite volume integration of the governing equation is carried out over a control volume and also over a finite time step ∆t. $\backslash int\backslash limits\_\; \backslash !\backslash !\backslash !\backslash int\_t^\; (\backslash frac\; \backslash ,dt)\backslash ,dV\; +\; \backslash int\_t^\; \backslash !\backslash !\backslash !\backslash int\backslash limits\_A\; (n.\; \backslash ,dA)\backslash ,dt\; =\; \backslash int\_t^\; \backslash !\backslash !\backslash !\backslash int\backslash limits\_A\; (n.(\backslash Gamma\; \backslash operatorname\; \backslash phi)\backslash ,dA)\backslash ,dt\; +\backslash int\_t^\; \backslash !\backslash !\backslash !\backslash int\backslash limits\_\; S\_\backslash phi\backslash ,dV\backslash ,dt$ The control volume integration of the steady part of the equation is similar to the steady state governing equation’s integration. We need to focus on the integration of the unsteady component of the equation. To get a feel of the integration technique, we refer to the one-dimensional unsteady heat conduction equation.〔An Introduction to COmputational Fluid Dynamics H. K. Versteeg and W Malalasekera Chapter 8 page 169〕 $\backslash rho\; c\; \backslash frac\; =\; \backslash frac\}\; +\; S$ $\backslash int\_t^\; \backslash !\backslash !\backslash !\backslash int\backslash limits\_\; \backslash rho\; c\; \backslash frac\; \backslash ,dV\backslash ,dt\; =\; \backslash int\_t^\; \backslash !\backslash !\backslash !\backslash int\backslash limits\_\; \backslash frac\}\; \backslash ,dV\backslash ,dt\; +\; \backslash int\_t^\; \backslash !\backslash !\backslash !\backslash int\backslash limits\_\; S\backslash ,dV\backslash ,dt$ $\backslash int\_e^w\; \backslash !\backslash !\backslash !\backslash int\_t^\; (\backslash rho\; c\; \backslash frac\; \backslash ,dt)\backslash ,dV\; =\; \backslash int\_t^\; ((k\; A\; \backslash frac\; )\_e\; -\; (k\; A\; \backslash frac\; )\_w)\backslash ,dt\; +\; \backslash int\_t^\; \backslash bar\; S\backslash Delta\; V\; \backslash ,dt$ Now, holding the assumption of the temperature at the node being prevalent in the entire control volume, the left side of the equation can be written as 〔(【引用サイトリンク】title=A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids )〕 $\backslash int\backslash limits\_\; \backslash !\backslash !\backslash !\backslash int\_t^\; (\backslash rho\; c\; \backslash frac\; \backslash ,dt)\backslash ,dV\; =\; \backslash rho\; c(T\_P\; -\; ^O)\; \backslash Delta\; V$ By using a first order backward differencing scheme, we can write the right hand side of the equation as $\backslash rho\; c\; (T\_P\; -\; ^0)\; \backslash Delta\; V\; =\; \backslash int\_t^\; (K\_e\; A\; \backslash frac\; \backslash bar\; S\backslash Delta\; V\; \backslash ,dt$ Now to evaluate the right hand side of the equation we use a weighting parameter $\backslash theta$ between 0 and 1, and we write the integration of $T\_P$ $I\_T\; =\; \backslash int\_t^\; T\_P\; \backslash ,dt\; =\; (\backslash theta\; T\_P\; -\; (1\; -\; \backslash theta\; )\; ^0)\; \backslash Delta\; t$ Now, the exact form of the final discretised equation depends on the value of $\backslash Theta$. As the variance of $\backslash Theta$ is 0< $\backslash Theta$ <1, the scheme to be used to calculate $T\_P$ depends on the value of the $\backslash Theta$ 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「Finite volume method for unsteady flow」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.