翻訳と辞書 Words near each other ・ Upwardly Global ・ Upwardly Mobile ・ Upwards (album) ・ Upware ・ Upwell ・ Upwell railway station (Upwell Tramway) ・ Upwelling ・ Upwey ・ Upwey (Abbotsbury Railway) railway station ・ Upwey (Dorset) railway station ・ Upwey railway station ・ Upwey railway station, Melbourne ・ Upwey Wishing Well Halt railway station ・ Upwey, Dorset ・ Upwey, Victoria ・ Upwind differencing scheme for convection ・ Upwind scheme ・ Upwood ・ Upwood Meadows ・ Upwords ・ Upwork ・ Upworldly Mobile ・ Upworthy ・ UPX ・ Upyna ・ Upytė ・ Upytė (Tatula) ・ UPZ ・ Upía River ・ Upír z Feratu Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Upwind differencing scheme for convection ： ウィキペディア英語版 Upwind differencing scheme for convection The upwind differencing scheme is a method used in numerical methods in computational fluid dynamics for convection–diffusion problems. This scheme is specific for Peclet number greater than 2 or less than −2 ==Description== The upwind differencing scheme by taking into account the direction of the flow overcomes that inability of the central differencing scheme. This scheme is developed for strong convective flows with suppressed diffusion effects. Also known as ‘Donor Cell’ Differencing Scheme, the convected value of property ф at the cell face is adopted from the upstream node. It can be described by Steady convection-diffusion partial Differential Equation〔H.K Versteeg & W. Malalasekera (1995). An introduction to Computational Fluid Dynamics.Chapter:5, Page103.〕〔Central differencing scheme#Steady-state convection diffusion equation〕 – : $\backslash frac(\backslash rho\backslash phi)+\backslash nabla\; \backslash cdot\; (\backslash rho\; \backslash mathbf\; \backslash phi)\backslash ,=\; \backslash nabla\; \backslash cdot\; (\backslash Gamma\backslash operatorname\; \backslash phi)+S\_$ Continuity equation: $\backslash left(\backslash rho\; u\; A\; \backslash right)\_\; -\; \backslash left(\backslash rho\; u\; A\; \backslash right)\_w\; =\; 0\; \backslash ,$〔H. K. Versteeg & W. Malalasekera (1995). ''An introduction to Computational Fluid Dynamics''. Chapter 5, page 104.〕〔Central differencing scheme#Formulation of Steady state convection diffusion equation〕 where $\backslash rho$ is density, $\backslash Gamma$ is diffusion coefficient, $\backslash mathbf$ is the velocity vector, $\backslash phi$ is the property to be computed, $S\_\backslash phi$ is the source term, and the subscripts $e$ and $w$ refer to the "east" and "west" faces of the cell (see Fig. 1 below). After discretization, applying continuity equation, and taking source term equals to zero we get〔Central differencing scheme#Formulation of Steady state convection diffusion equation〕 Central difference discretized equation : $F\_\; \backslash phi\_-F\_\; \backslash phi\_\backslash ,=\; D\_(\backslash phi\_-\backslash phi\_)-D\_(\backslash phi\_-\backslash phi\_)$ $\backslash ;$.〔H.K Versteeg & W. Malalasekera. An introduction to Computational Fluid Dynamics.Chapter:5. Page 105.〕.....(1) :$F\_-F\_\backslash ,=0$ $\backslash ;$〔H.K Versteeg & W. Malalasekera . An introduction to Computational Fluid Dynamics.Chapter:5. Page 105.〕.....(2) Lower case denotes the face and upper case denotes node; $E$, $W$, and $P$ refer to the "East," "West," and "Central" cell. (again, see Fig. 1 below). Defining variable F as convection mass flux and variable D as diffusion conductance :$F\backslash ,=\; \backslash rho\; u\; A$$\backslash ;$ and $\backslash ;$$D\backslash ,=\; \backslash frac$ $\backslash ;$ Peclet number (Pe) is a non-dimensional parameter determining the comparative strengths of convection and diffusion Peclet number: : $Pe\; \backslash ,=\; \backslash frac\; \backslash ,=\; \backslash frac$ $\backslash ;$ For a Peclet number of lower value (|Pe| < 2, diffusion is dominant and for this we use the central difference scheme. For other values of and upwind scheme is used for convection dominating flows with Peclet number (|Pe| > 2). For positive flow direction :$u\_\; >\; 0$ :$u\_\; >\; 0$ Corresponding upwind scheme equation: :$F\_\; \backslash phi\_-F\_\; \backslash phi\_\backslash ,=\; D\_(\backslash phi\_-\backslash phi\_)-D\_(\backslash phi\_-\backslash phi\_)$〔H.K Versteeg & W. Malalasekera . An introduction to Computational Fluid Dynamics.Chapter:5.Page 115.〕.....(3) Due to strong convection and suppressed diffusion :$\backslash phi\_\; \backslash ,=\; \backslash phi\_$〔H. K. Versteeg & W. Malalasekera ). ''An Introduction to Computational Fluid Dynamics, Chapter 5, page 115.〕 :$\backslash phi\_\; \backslash ,=\; \backslash phi\_$ Rearranging equation (3) gives :$(D\_+\; (F\_-F\_))\backslash phi\_\backslash ,\; =(D\_+F\_)\backslash phi\_+D\_\backslash phi\_)$$\backslash ;$ Identifying coefficients, :$a\_\backslash ,=\; (+\; F\_)\; +\; D\_\; +\; (F\_\; -\; F\_))$ $\backslash ;$ :$a\_\backslash ,=(D\_\; +\; F\_)$ :$a\_\backslash ,=\; D\_$ For negative flow direction : : Corresponding upwind scheme equation: :$F\_\; \backslash phi\_-F\_\; \backslash phi\_\backslash ,=\; D\_(\backslash phi\_-\backslash phi\_)-D\_(\backslash phi\_-\backslash phi\_)$〔H.K Versteeg & W. Malalasekera. An introduction to Computational Fluid Dynamics.Chapter:5. Page115.〕.....(4) :$\backslash phi\_\backslash ,=\; \backslash phi\_$ :$\backslash phi\_\backslash ,=\; \backslash phi\_$ Rearranging equation(4) gives :$(D\_e\; -\; F\_e\; )\; +\; D\_w\; +\; (\; F\_e\; -\; F\_w\; ))\; \backslash phi\_\; =\; D\_w\; \backslash phi\_\; +\; (\; D\_e\; -\; F\_e\; )\; \backslash phi\_$ Identifying coefficients, :$a\_\backslash ,=\; D\_$ :$a\_\backslash ,=\; D\_\; -\; F\_$ We can generalize coefficients as〔H. K. Versteeg & W. Malalasekera. ''An Introduction to Computational Fluid Dynamics'', Chapter 5, page 116.〕 – :$a\_=D\_\; +\; \backslash max(F\_,0)$ 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「Upwind differencing scheme for convection」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.