Non‐intrusive reduced‐order modeling for multiphase porous media flows using Smolyak sparse grids. (23rd June 2016)

• Record Type: Journal Article
• Authors: Xiao, Dunhui; Lin, Zhi; Fang, Fangxin; Pain, Christopher C.; Navon, Ionel M.; Salinas, Pablo; Muggeridge, Ann
• Is Part Of: International journal for numerical methods in fluids. Volume 83:Number 2(2017)
• Page Start: 205
• Page End: 219
• Publication Date: 2016-06-23
• Subjects: non‐intrusive -- Smolyak sparse grid -- POD -- multiphase -- porous media; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4263
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: In this article, we describe a non‐intrusive reduction method for porous media multiphase flows using Smolyak sparse grids. This is the first attempt at applying such an non‐intrusive reduced‐order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. The advantage of this NIROM for porous media multiphase flows resides in that its non‐intrusiveness, which means it does not require modifications to the source code of full model. Another novelty is that it uses Smolyak sparse grids to construct a set of hypersurfaces representing the reduced‐porous media multiphase problem. This NIROM is implemented under the framework of an unstructured mesh control volume finite element multiphase model. Numerical examples show that the NIROM accuracy relative to the high‐fidelity model is maintained, whilst the computational cost is reduced by several orders of magnitude. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : In this article, we describe a non‐intrusive reduction method for porous media multiphase flows using Smolyak sparse grids.This is the first attempt at applying such an non‐intrusive reduced order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. This NIROM is implemented under the framework of an unstructured mesh control volume finite element multiphase model. Numerical examples show that the NIROM accuracy relative to the high‐fidelity model is maintained, whilst the computational cost is reduced by several orders of magnitude. The figures displayed earlier (left) show the saturation solutions of the high‐permeability domain embedded in a low‐permeability domain problem at time instances 0.05. The solutions compare the predictions from non‐intrusive reduced order model with high‐fidelity full model using 36 proper orthogonal decomposition basis functions.