Abstract This work presents an overview of techniques that enable the construction of collocated finite volume method for complex multi-physics models in multiple domains. Each domain is characterized by the properties of heterogeneous media and features a distinctive multi-physics model. Coupling together systems of equations, corresponding to multiple unknowns, results in a vector flux. The finite volume method requires continuity of intradomain and interdomain vector fluxes. The continuous flux is derived using an extension of the harmonic averaging point concept. Often, the collocated coupling of the equations results in a saddle-point problem subject to inf-sup stability issues. These issues are addressed by the eigen-splitting of indefinite matrix coefficients encountered in the flux expression. The application of the techniques implemented within INMOST platform to hydraulic fracturing problem is demonstrated.

中文翻译：

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用于INMOST平台内水力压裂建模的多物理场通量耦合

摘要 这项工作概述了能够为多个域中的复杂多物理场模型构建并置有限体积方法的技术。每个域都具有异构介质的特性，并具有独特的多物理模型。将对应于多个未知数的方程组耦合在一起会产生矢量通量。有限体积方法需要域内和域间矢量通量的连续性。连续通量是使用谐波平均点概念的扩展导出的。通常，方程的并置耦合会导致受 inf-sup 稳定性问题影响的鞍点问题。这些问题通过通量表达式中遇到的不定矩阵系数的特征分裂来解决。