The uncertainty quantification (UQ) for partial differential equations (PDEs) with random parameters is important for science and engineering. Forward UQ quantifies the impact of random parameters on the solution or the quantity-of-interest (QoI). In the current study, we propose a new extension of the stochastic finite volume (SFV) method by clustering samples in the parameter space. Compared to classic SFV based on structured grid in the parameter space, the new scheme based on clustering extends SFV to parameter spaces of higher dimensions. This paper presents the construction of SFV schemes for typical parametric elliptic, parabolic and hyperbolic equations for Darcy flows in porous media, as well as the error analysis, demonstration and validation of the new extension using typical reservoir simulation test cases.

翻译：偏微分方程随机参数的不确定性量化在科学与工程领域具有重要意义。前向不确定性量化旨在评估随机参数对解或关注量的影响。本研究提出了一种基于参数空间样本聚类的随机有限体积方法新扩展。相较于传统基于参数空间结构化网格的随机有限体积方法，这种基于聚类的新方案将随机有限体积方法扩展到了更高维度的参数空间。本文针对多孔介质达西流中的典型参数化椭圆型、抛物型和双曲型方程，阐述了随机有限体积方案的构建过程，并通过典型油藏模拟测试案例对新扩展方法进行了误差分析、论证与验证。