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首页> 外文期刊>Journal of Computational Physics >A predictor-corrector algorithm for the coupling of stiff ODEs to a particle population balance
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A predictor-corrector algorithm for the coupling of stiff ODEs to a particle population balance

机译：一种将硬ODE耦合到粒子总体平衡的预测校正算法

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In this paper a novel predictor-corrector algorithm is presented for the solution of coupled gas-phase - particulate systems. The emphasis of this work is the study of soot formation, but the concepts can be applied to other systems. This algorithm couples a stiff ODE solver to a Monte Carlo population balance solver. Such coupling has been achieved previously for similar systems using a Strang operator splitting algorithm, however, that algorithm demonstrated several numerical issues which resulted in a high computational cost to acquire adequate precision. In particular a source-sink instability was identified whereby a large-magnitude source term present in the ODE system was competing with a similarly sized sink term in the population balance. This instability required that the splitting step size was very small in order to keep numerical error sufficiently low. A predictor-corrector algorithm has been formulated to negate this instability. An additional efficiency is gained with this algorithm as a principal computational cost of the Strang splitting algorithm is removed: the requirement to re-initialise the ODE solver every splitting step. The numerical convergence of the new algorithm is demonstrated, and its efficiency is compared to that of the Strang splitting algorithm. Substantial computation time savings are demonstrated, which allow a fixed error in three studied system functionals to be achieved with an order-of-magnitude reduction in computation time. (C) 2008 Elsevier Inc. All rights reserved.
机译：在本文中，提出了一种新颖的预测器-校正器算法，用于求解气相-颗粒耦合系统。这项工作的重点是研究烟灰的形成，但是这些概念可以应用于其他系统。该算法将刚性ODE求解器耦合到Monte Carlo总体平衡求解器。以前已经使用Strang算子拆分算法为类似的系统实现了这种耦合，但是，该算法演示了几个数值问题，导致获得足够的精度需要很高的计算成本。尤其是，确定了源汇不稳定性，从而使ODE系统中存在的一个大震级源项与人口平衡中大小相似的汇项相竞争。这种不稳定性要求分裂步长非常小，以使数值误差保持足够低。已经制定了预测器-校正器算法来消除这种不稳定性。通过消除Strang拆分算法的主要计算成本，使用该算法可获得更高的效率：每个拆分步骤都需要重新初始化ODE求解器。证明了新算法的数值收敛性，并将其效率与Strang分裂算法进行了比较。展示了可观的计算时间节省，通过减少计算时间的数量级，可以实现三个已研究系统功能的固定错误。 （C）2008 Elsevier Inc.保留所有权利。

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