A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media. (English) Zbl 1378.76109
Summary: 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.
MSC:
| 76S05 | Flows in porous media; filtration; seepage |
| 76T99 | Multiphase and multicomponent flows |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M75 | Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs |
Keywords:
adaptive stochastic collocation method; nested sparse grids; two-stage approach; multiphase flow; heterogeneous porous mediaReferences:
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