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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 Temporal discretization ： ウィキペディア英語版 Temporal discretization In case of transient problems, the simulations conducted using computer-aided engineering (CAE) packages require discretizing the governing equations both in space and time. Such problems are unsteady (e.g. flow problems) and therefore provide solution which varies with time for a particular position. Temporal discretization involves the integration of every term in different equations over a time step (Δt). The spatial domain can be discretized to produce a semi-discrete form: : $\backslash frac(x,t)\; =\; F(\backslash varphi).~$ If the discretization is done using backward differences; The first order temporal discretization is given as:〔(Selection of Spatial and Temporal discretization )〕 : $\backslash frac\}\; =\; F(\backslash varphi),$ And the second order discretization is given as: : $\backslash frac+\backslash varphi^\}\; =\; F(\backslash varphi),$ where φ = a scalar quantity. n+1 = value at the next time level,t+Δt. n = value at the current time level,t. n-1 = value at the previous time level, t-Δt. The function F($\backslash varphi$) is evaluated using implicit and explicit time integration. == Description == The temporal discretization is done through integration over time on the general discretized equation. First, values at a given control volume P at time interval t are assumed and then value at time interval t+Δt is found. This method states that the time integral of a given variable is equal to a weighted average between current and future values. The integral form of the equation can be written as: : $\backslash frac\}\; =\; f.F(\; \backslash varphi^)\; +\; (1-f).F(\; \backslash varphi^\; ),$ where f is weighing factor ranges between 0 and 1. If f = 0.0 results in the fully explicit scheme. f = 1.0 results in the fully implicit scheme. f = 0.5 results in the Crank-Nicolson scheme. For any control volume this integration holds true for any discretized variable. The following equation is obtained when applied to the governing equation including full discretized diffusion, convection, and source terms. : $\backslash int\backslash limits\_^\; F(\backslash varphi)\; dt\; =\; (f.\; F\_\backslash varphi^\; +\; (1-f).\; F\_\backslash varphi^t)\; \backslash Delta\; t$ 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「Temporal discretization」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.