A dynamic multi-timescale method for combustion modeling with detailed and reduced chemical kinetic mechanisms

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XiaolongGouabWentingSunaZhengChenacYiguangJua https://www.sciencedirect.com/science/article/pii/S001021801000074X#!

Abstruct

A new on-grid dynamic multi-timescale (MTS) method is presented to increase significantly the computation efficiency involving multi-physical and chemical processes using detailed and reduced kinetic mechanisms. The methodology of the MTS method using the instantaneous timescales of different species is introduced. The definition of the characteristic time for species is examined and compared with that of the computational singular perturbation (CSP) and frozen reaction rate methods by using a simple reaction system. A hybrid multi-timescale (HMTS) algorithm is constructed by integrating the MTS method with an implicit Euler scheme, respectively, for species with and without the requirement of accurate time histories at sub-base timescales. The efficiency and the robustness of the MTS and HMTS methods are demonstrated by comparing with the Euler and VODE solvers for homogenous ignition and unsteady flame propagation of hydrogen, methane, and n-decane–air mixtures. The results show that both MTS and HMTS reproduce well the species and temperature histories and are able to decrease computation time by about one-order with the same kinetic mechanism. Compared to MTS, HMTS has slightly better computation efficiency but scarifies the stability at large base time steps. The results also show that with the increase of mechanism size and the decrease of time step, the computation efficiency of multi-timescale method increases compared to the VODE solver. In addition, it is shown that the integration of the multi-timescale method with the path flux analysis based mechanism reduction approach can further increase the computation efficiency. Unsteady simulations of outwardly propagating spherical n-decane–air premixed flames demonstrate that the multi-timescale method is rigorous for direct numerical simulations with both detailed and reduced chemistry and can dramatically improve the computation efficiency.

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要点

• マルチタイムスケール手法（MTS）を提案した
• 異なる化学種のその時刻における時間スケールを用いている
• 計算機的な特異摂動（CSP）と凍結された反応速度法を用いた
• MTSとオイラー陰解法を合体したハイブリッドMTS（HMTS）を構築した

  疑問点

• 陰解法を組み合わせる理由
• CSPとは何か
• 凍結された化学反応は，特性時間が長い反応をほっとくということ？

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燃焼現象における時間スケールの図．こういうの書きたい

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仮説

Are there any simple and alternative methods which can efficiently integrate a multi-timescale problem and retain the transient information of species and physical processes at different timescales.

だがしかし

A convenient way to obtain time accurate solution of various reaction groups is the Euler method. However, an explicit Euler method needs a time-marching step smaller than the smallest timescale in a physical process

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化学反応の特性時間の式

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MTSとHMTSの違い

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• CSP methodは行列演算を使って少しややこしい式変形の末に，化学反応の特性時間が得られる．式を見てみたけど，一見飛躍しているように思えるような変形をしていた．
• 凍結された化学反応法は，単純に，化学種組成Yを時間微分項dY/dtで割ることで計算する．ただし平衡状態ではゼロ割になることが問題

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• 陰解法を使う理由は，化学反応の特性時間を気にせずに，計算機が勝手にいい感じの時間ステップで計算してくれることによる正確さ．遅い化学反応については，特性時間よりも小さければ陽的に解いても問題は少ないのでそうしているという気持ち？そして，計算ステップをそろえるためにもそのほうが便利という解釈でいいのかしら

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森井先生の解説 http://www.combustionsociety.jp/fullpaper/176pdf/176_2.pdf 森井先生の解説２：陽解法からERENAまで http://www.nagare.or.jp/download/noauth.html?d=34-2tokushu11.pdf&dir=87 寺島先生の解説 http://www.combustionsociety.jp/fullpaper/174pdf/174_3.pdf

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CFDに組み込むことを考えたときに，陰解法では初期化のプロセスが繰り返されるために，計算の効率が悪いらしい（0次元解析と比較して）．その解決のために，近年のMTSやQSSを用いた陽解法たちの開発が進んで切るらしい． 僕がこれからやることとしては

• 0次元解析のための陰解法による計算
• CFD解析のための陽解法による計算 の二つができたら素敵だわね