A Reduced Basis Method for Darcy flow systems that ensures local mass conservation by using exact discrete complexes

2022/05/31 by Wietse M. Boon, Boon, Wietse M., Alessio Fumagalli +1
Engineering · Physics and Astronomy · #55U15 #65N22 #65N30 #76M10 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2205.15626

openalex publication_date 2022/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

A solution technique is proposed for flows in porous media that guarantees local conservation of mass. We first compute a flux field to balance the mass source and then exploit exact co-chain complexes to generate a solenoidal correction. A reduced basis method based on proper orthogonal decomposition is employed to construct the correction and we show that mass balance is ensured regardless of the quality of the reduced basis approximation. The method is directly applicable to mixed finite and virtual element methods, among other structure-preserving discretization techniques, and we present the extension to Darcy flow in fractured porous media.

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