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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 Conservation form ： ウィキペディア英語版 Conservation form Conservation form or ''Eulerian form'' refers to an arrangement of an equation or system of equations, usually representing an hyperbolic system, that emphasizes that a property represented is conserved, i.e. a type of continuity equation. The term is usually used in the context of continuum mechanics. == General form == Equations in conservation form take the form :$\backslash frac\; +\; \backslash nabla\; \backslash cdot\; f(\backslash xi)\; =\; 0$ for any conserved quantity $\backslash xi$, with a suitable function $f$. An equation of this form can be transformed into an integral equation :$\backslash frac\; d\; \backslash int\_V\; \backslash xi\; dV\; +\; \backslash int\_\; f(\backslash xi)\; \backslash cdot\; \backslash nu\; ~\; dS$ using the divergence theorem. The integral equation states that the change rate of the integral of the quantity $\backslash xi$ over an arbitrary control volume $V$ is given by the flux $f(\backslash xi)$ through the boundary of the control volume, with $\backslash nu$ being the surface normal through the boundary. $\backslash xi$ is neither produced nor consumed inside of $V$ and is hence conserved. A typical choice for $f$ is $f(\backslash xi)\; =\; \backslash xi\; \backslash bold\; u$, with velocity $\backslash bold\; u$, meaning that the quantity $\backslash xi$ flows with a given velocity field. The integral form of such equations is usually the physically more natural formulation, and the differential equation arises from differentiation. Since the integral equation can also have non-differentiable solutions, the equality of both formulations can break down in some cases, leading to weak solutions and severe numerical difficulties in simulations of such 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「Conservation form」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.