A reduction scheme for coupled multicomponent transport‐reaction problems in porous media: Generalization to problems with heterogeneous equilibrium reactions
A reduction scheme for coupled multicomponent transport‐reaction problems in porous media: Generalization to problems with heterogeneous equilibrium reactions
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多孔介质中耦合多组分输运反应问题的简化方案：异质反应平衡问题的推广
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发表时间：
2007
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通讯作者：
P. Knabner
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作者：
S. Kräutle;P. Knabner
本文提出了一种有效计算多组分、多反应体系的输运和反应的系统方法。这种方法的目的是重新表述给定的微分或微分代数方程组，使得耦合和非线性集中在减少的方程数量中（如果与原始公式相比），而一些线性方程与系统解耦。由此产生的系统处理的精神，一个全球性的隐式方法（“一步法”），避免运营商分裂技术。本文中提出的问题大小的减少有助于限制此类问题的数值模拟的大计算成本。减少机制是在以前的文件中提出的方法的推广。现在，混合的移动的/非移动的物种，均相/非均相动力学/平衡反应的问题被认为是，而以前的出版物被限制到没有非均相平衡反应（如平衡吸附）的问题。一个应用程序的减少机制的一个例子的问题，以调查减少耦合的非线性方程组的数量，并比较它与其他方法。
In this article a systematic approach for the efficient computation of the transport and reaction of a multispecies, multireaction system is proposed. The objective of this approach is to reformulate the given system of differential or differential‐algebraic equations in such a way that the couplings and the nonlinearities are concentrated in a reduced number of equations (if compared to the original formulation), while some linear equations decouple from the system. The resulting system is handled in the spirit of a global implicit approach (“one step method”) avoiding operator splitting techniques. The reduction of the problem size proposed in this article helps to limit the large computational costs of numerical simulations for such problems. The reduction mechanism is a generalization of the method proposed in a previous paper. Now, problems with mixed mobile/immobile species, homogeneous/heterogeneous kinetic/equilibrium reactions are considered, while the previous publication was restricted to problems without heterogeneous equilibrium reactions (such as equilibrium sorption). An application of the reduction mechanism to an example problem is given in order to investigate the reduction of the number of coupled nonlinear equations and to compare it to other methods.