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In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…

Numerical Analysis · Mathematics 2019-08-02 Denis Spiridonov , Maria Vasilyeva , Eric T. Chung

We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a…

Numerical Analysis · Mathematics 2016-06-22 Camille Negrello , Pierre Gosselet , Christian Rey , Julien Pebrel

In this work, phase-field modeling of hydraulic fractures in porous media is extended towards a global-local approach. Therein, the failure behavior is solely analyzed in a (small) local domain. In the surrounding medium, a simplified and…

Numerical Analysis · Mathematics 2020-01-20 Fadi Aldakheel , Nima Noii , Thomas Wick , Peter Wriggers

We address the discretization of two-phase Darcy flows in a fractured and deformable porous medium, including frictional contact between the matrix-fracture interfaces. Fractures are described as a network of planar surfaces leading to the…

Numerical Analysis · Mathematics 2022-01-24 Francesco Bonaldi , Jérôme Droniou , Roland Masson , Antoine Pasteau

The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular…

Computational Engineering, Finance, and Science · Computer Science 2023-08-23 Roman Vodička

In this work we present the mathematical models for single-phase flow in fractured porous media. An overview of the most common approaches is considered, which includes continuous fracture models and discrete fracture models. For the…

Computational Physics · Physics 2020-04-01 Luca Formaggia , Anna Scotti , Alessio Fumagalli

In this work, we consider fracture propagation in nearly incompressible and (fully) incompressible materials using a phase-field formulation. We use a mixed form of the elasticity equation to overcome volume locking effects and develop a…

Numerical Analysis · Mathematics 2022-02-10 Timo Heister , Katrin Mang , Thomas Wick

Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme…

Numerical Analysis · Mathematics 2024-12-20 Hanyu Li , Mary F. Wheeler

Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…

Numerical Analysis · Mathematics 2025-02-25 Dilong Zhou , Rafael Guiraldello , Felipe Pereira

Fluid-induced slip of fractures is characterized by strong multiphysics couplings. Three physical processes are considered: Flow, rock deformation and fracture deformation. The fractures are represented as lower-dimensional objects embedded…

Geophysics · Physics 2017-12-19 Runar L. Berge , Inga Berre , Eirik Keilegavlen

We extend the Balancing Domain Decomposition by Constraints (BDDC) method to flows in porous media discretised by mixed-hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are…

Numerical Analysis · Mathematics 2015-11-24 Jakub Šístek , Jan Březina , Bedřich Sousedík

Numerical simulations of flow and transport in porous media usually rely on hybrid-dimensional models, i.e., the fracture is considered as objects of a lower dimension compared to the embedding matrix. Such models are usually combined with…

Numerical Analysis · Mathematics 2020-11-18 Maria Giuseppina Chiara Nestola , Marco Favino

In this paper, we consider a non-local (in time) two-phase flow model. The non-locality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed-point iterative linearization…

Computational Physics · Physics 2019-10-02 Abay M. Kassa , Kundan Kumar , Sarah E. Gasda , Florin A. Radu

This work considers a Stokes flow in a deformable fracture interacting with a linear elastic medium. To this end, we employ a phase-field model to approximate the crack dynamics. Phase-field methods belong to interface-capturing approaches…

Numerical Analysis · Mathematics 2024-04-15 Henry von Wahl , Thomas Wick

In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…

Numerical Analysis · Mathematics 2020-04-22 Maria Vasilyeva , Wing T. Leung , Eric T. Chung , Yalchin Efendiev , Mary Wheeler

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Numerical Analysis · Mathematics 2026-01-09 Jiaming Guo , Dunhui Xiao

In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…

Numerical Analysis · Mathematics 2025-09-12 Siu Wun Cheung , Eric T. Chung , Yalchin Efendiev , Eduardo Gildin , Yating Wang , Jingyan Zhang

The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM uses the so-called hybrid-dimensional approach to treat fractures explicitly as low-dimensional entries (e.g.…

Numerical Analysis · Mathematics 2021-02-01 Ziyao Xu , Yang Yang

We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in…

In this paper, our aim is to present (1) an embedded fracture model (EFM) for coupled flow and mechanics problem based on the dual continuum approach on the fine grid and (2) an upscaled model for the resulting fine grid equations. The…

Numerical Analysis · Mathematics 2018-11-14 Maria Vasilyeva , Eric T. Chung , Yalchin Efendiev , Jihoon Kim