Comparative study of modelling flows in porous media for engineering applications using finite volume and artificial neural network methods

• Published in: Engineering with computers Vol. 39; no. 6; pp. 3773 - 3789
• Main Authors: Makauskas, Pijus, Pal, Mayur, Kulkarni, Vismay, Kashyap, Abhishek Singh, Tyagi, Himanshu
• Format: Journal Article
• Language: English
• Published: London Springer London 01.12.2023; Springer Nature B.V
• Subjects: Algorithms; Approximation; Artificial neural networks; Boundary conditions; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Comparative studies; Computer Science; Computer-Aided Engineering (CAD; Control; Deep learning; Engineering; Finite volume method; Geometry; Machine learning; Math. Applications in Chemistry; Mathematical and Computational Engineering; Neural networks; Original Article; Partial differential equations; Permeability; Porous media; Single-phase flow; Systems Theory; Tensors; Heterogeneous; CNN; Elliptic equation; finite-volume method; Neural PDE
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-023-01814-x

A neural solution methodology, using a feed-forward and a convolutional neural networks, is presented for general tensor elliptic pressure equation with discontinuous coefficients. The methodology is applicable for solving single-phase flow in porous medium, which is traditionally solved using numerical schemes like finite-volume methods. The neural solution to elliptic pressure equation is based on machine learning algorithms and could serve as a more effective alternative to finite volume schemes like two-point or multi-point discretization schemes (TPFA or MPFA) for faster and more accurate solution of elliptic pressure equation. Series of 1D and 2D test cases, where the results of Neural solutions are compared to numerical solutions obtained using two-point schemes with range of heterogeneities, are also presented to demonstrate general applicability and accuracy of the Neural solution method.