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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 Power law scheme ： ウィキペディア英語版 Power law scheme The power law scheme was first used by Suhas Patankar (1980). It helps in achieving approximate solutions in computational fluid dynamics (CFD) and it is used for giving a more accurate approximation to the one-dimensional exact solution when compared to other schemes in computational fluid dynamics (CFD). This scheme is based on the analytical solution of the convection diffusion equation. This scheme is also very effective in removing False diffusion error. == Working == The power-law scheme interpolates the face value of a variable, $\backslash phi\backslash ,$, using the exact solution to a one-dimensional convection-diffusion equation given below: :$\backslash frac(\backslash rho\; u\; \backslash phi)\backslash ,=\; \backslash frac\backslash Gamma\backslash frac$ In the above equation Thermal Diffusivity, $\backslash Gamma$ and both the density $\backslash rho$ and velocity remains constant u across the interval of integration. Integrating the equation, with Boundary Conditions, :$\backslash phi\_0\backslash ,=\; \backslash phi\; |\_(x=0)$ :$\backslash phi\_L\backslash ,=\; \backslash phi\; |\_(x=L)$ Variation of face value with distance, x is given by the expression, $\backslash frac\backslash ,=\; \backslash frac)\}$ where Pe is the Peclet number given by $P\_e\backslash ,=\; \backslash frac$ Peclet number is defined to be the ratio of the rate of convection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient. The variation between $\backslash phi\backslash ,$ and x is depicted in Figure for a range of values of the Peclet number. It shows that for large Pe, the value of $\backslash phi\backslash ,$ at x=L/2 is approximately equal to the value at upwind boundary which is assumption made by the upwind differencing scheme. In this scheme diffusion is set to zero when cell Pe exceeds 10. This implies that when the flow is dominated by convection, interpolation can be completed by simply letting the face value of a variable be set equal to its ``upwind'' or upstream value. When Pe=0 (no flow, or pure diffusion), Figure shows that solution, $\backslash phi\backslash ,$ may be interpolated using a simple linear average between the values at x=0 and x=L. When the Peclet number has an intermediate value, the interpolated value for $\backslash phi\backslash ,$ at x=L/2 must be derived by applying the ``power law'' equivalent. The simple average convection coefficient formulation can be replaced with a formula incorporating the power law relationship : where F = $\backslash rho$u and D = $\backslash Gamma$/x Fl,Dl and Fr,Dr are the properties on the left node and right node respectively. The central coefficient is given by ac=al+ar+(Fr-Fl) 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「Power law scheme」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.