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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 Flux limiter ： ウィキペディア英語版 Flux limiter Flux limiters are used in high resolution schemes – numerical schemes used to solve problems in science and engineering, particularly fluid dynamics, described by partial differential equations (PDE's). They are used in high resolution schemes, such as the MUSCL scheme, to avoid the spurious oscillations (wiggles) that would otherwise occur with high order spatial discretization schemes due to shocks, discontinuities or sharp changes in the solution domain. Use of flux limiters, together with an appropriate high resolution scheme, make the solutions total variation diminishing (TVD). Note that flux limiters are also referred to as slope limiters because they both have the same mathematical form, and both have the effect of limiting the solution gradient near shocks or discontinuities. In general, the term flux limiter is used when the limiter acts on system ''fluxes'', and slope limiter is used when the limiter acts on system ''states'' (like pressure, velocity etc.). ==How they work== The main idea behind the construction of flux limiter schemes is to limit the spatial derivatives to realistic values – for scientific and engineering problems this usually means physically realisable and meaningful values. They are used in high resolution schemes for solving problems described by PDEs and only come into operation when sharp wave fronts are present. For smoothly changing waves, the flux limiters do not operate and the spatial derivatives can be represented by higher order approximations without introducing spurious oscillations. Consider the 1D semi-discrete scheme below, :$\backslash frac\; +\; \backslash frac\; \backslash left($ F \left( u_} \right) - F \left( u_} \right) \right ) =0, where, $F\; \backslash left(\; u\_\}\; \backslash right)\; \backslash$ and $F\; \backslash left(\; u\_\}\; \backslash right)\; \backslash$ represent edge fluxes for the ''ith'' cell. If these edge fluxes can be represented by ''low'' and ''high'' resolution schemes, then a flux limiter can switch between these schemes depending upon the gradients close to the particular cell, as follows, :$F\; \backslash left(\; u\_\}\; \backslash right)\; =\; f^\_\}\; -\; \backslash phi\backslash left(\; r\_i\; \backslash right)$ \left( f^_} - f^_} \right), :$F\; \backslash left(\; u\_\}\; \backslash right)\; =\; f^\_\}\; -\; \backslash phi\backslash left(\; r\_\; \backslash right)$ \left( f^_} - f^_} \right), where :$f^\; =\; \backslash$ low precision, high resolution flux, :$f^\; =\; \backslash$ high precision, low resolution flux, :$\backslash phi\backslash \; (r)\; =\; \backslash$ flux limiter function, and $r\backslash$ represents the ratio of successive gradients on the solution mesh, i.e., :$r\_\; =\; \backslash frac\}\}$. The limiter function is constrained to be greater than or equal to zero, i.e., $\backslash phi\backslash \; (r)\; \backslash ge\; 0$. Therefore, when the limiter is equal to zero (sharp gradient, opposite slopes or zero gradient), the flux is represented by a ''low resolution scheme''. Similarly, when the limiter is equal to 1 (smooth solution), it is represented by a ''high resolution scheme''. The various limiters have differing switching characteristics and are selected according to the particular problem and solution scheme. No particular limiter has been found to work well for all problems, and a particular choice is usually made on a trial and error basis. 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「Flux limiter」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.