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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 two dimensional diffusion problem ： ウィキペディア英語版 Finite volume method for two dimensional diffusion problem The methods used for solving two dimensional Diffusion problems are similar to those used for one dimensional problems. The general equation for steady diffusion can be easily be derived from the general transport equation for property ''Φ'' by deleting transient and convective terms $\backslash fracx\}\backslash left(\backslash Gamma\}\backslash right)+\backslash fracy\}\backslash left(\backslash Gamma\}\backslash right)+S=0$ where, $\backslash Gamma$ is the Diffusion coefficient and $S$ is the Source term. A portion of the two dimensional grid used for Discretization is shown below: In addition to the east (E) and west (W) neighbors, a general grid node P , now also has north (N) and south (S) neighbors. The same notation is used here for all faces and cell dimensions as in one dimensional analysis. When the above equation is formally integrated over the Control volume, we obtain $\backslash int\_\}\backslash left(\backslash Gamma\}\backslash right)dx.dy+\backslash int\_\}\backslash left(\backslash Gamma\}\backslash right)dx.dy+\backslash int\_\}dV=0$ Using the divergence theorem, the equation can be rewritten as : $$ \left()+\left()+\bar\Delta}_w= }_p- Flux across the east face = $$ _eA_e\left(\frac}_e= }_e- Flux across the south face = $$ _sA_s\left(\frac}_s= }_p- Flux across the north face = $$ _nA_n\left(\frac}_n= }_n- Substituting these expressions in equation (2) we obtain $$ }_e- - }_p- + }_n- - }_p-+ \bar\DeltaV = S_u + S_p *S_ , this equation can be rearranged as, + \frac_nA_n} + \frac_sA_s} - S_p\right ) \phi\phi\phi\phi\phi_W + a_E \phi_N + S_u Where, || $\backslash frac\_eA\_e\}$ || $\backslash frac\_sA\_s\}$ || $\backslash frac\_nA\_n\}$ || $a\_W+a\_E+a\_S+a\_N-S\_p$ |} The face areas in y two dimensional case are : $A\_\; =\; A\_\; =\; \backslash Delta\; =\; \backslash Delta$ and $S\_$ terms. Subsequently the resulting set of equations is solved to obtain the two dimensional distribution of the property $\backslash varphi\{\}$ ==References== * Patankar, Suhas V. (1980), Numerical Heat Transfer and Fluid Flow, Hemisphere. * Hirsch, C. (1990), Numerical Computation of Internal and External Flows, Volume 2: Computational Methods for Inviscid and Viscous Flows, Wiley. * Laney, Culbert B.(1998), Computational Gas Dynamics, Cambridge University Press. * LeVeque, Randall(1990), Numerical Methods for Conservation Laws, ETH Lectures in Mathematics Series, Birkhauser-Verlag. * Tannehill, John C., et al., (1997), Computational Fluid mechanics and Heat Transfer, 2nd Ed., Taylor and Francis. * Wesseling, Pieter(2001), Principles of Computational Fluid Dynamics, Springer-Verlag. * Carslaw, H. S. and Jager, J. C. (1959). Conduction of Heat in Solids. Oxford: Clarendon Press * Crank, J. (1956). The Mathematics of Diffusion. Oxford: Clarendon Press * Thambynayagam, R. K. M (2011). The Diffusion Handbook: Applied Solutions for Engineers: McGraw-Hill 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 two dimensional diffusion problem」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.