A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

详细信息    查看全文

• 作者：Qinzhuo Liao^a ; ^{liaoqz@pku.edu.cn} ; Dongxiao Zhang^a ; Hamdi Tchelepi^b
• 关键词：Adaptive stochastic collocation method ; Nested sparse grids ; Two-stage approach ; Multiphase flow ; Heterogeneous porous media
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：330
• 期：Complete
• 页码：828-845
• 全文大小：4908 K
• 卷排序：330

文摘

A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod–Patterson–Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.