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A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local…

Numerical Analysis · Mathematics 2023-11-10 Luling Cao , Jian Li , Zhangxin Chen , Guangzhi Du

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

Numerical Analysis · Mathematics 2026-01-13 Jiaming Guo , Dunhui Xiao

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…

Numerical Analysis · Mathematics 2018-02-07 Camille Negrello , Pierre Gosselet , Christian Rey

We present an adaptive space-time mesh refinement approach based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments…

Numerical Analysis · Mathematics 2018-09-10 Gurpreet Singh , Mary F. Wheeler

We present a hybrid partitioned deep learning framework for the reduced-order modeling of fluid-structure interaction. Using the discretized Navier-Stokes in the arbitrary Lagrangian-Eulerian reference frame, we generate the full-order flow…

Fluid Dynamics · Physics 2021-11-02 Rachit Gupta , Rajeev Kumar Jaiman

Hydro-mechanical processes in rough fractures are highly non-linear and govern productivity and associated risks in a wide range of reservoir engineering problems. To enable high-resolution simulations of hydro-mechanical processes in…

An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe…

Numerical Analysis · Mathematics 2020-11-10 Luca Formaggia , Alessio Fumagalli , Anna Scotti

Developing robust simulation tools for problems involving multiple mathematical scales has been a subject of great interest in computational mathematics and engineering. A desirable feature to have in a numerical formulation for multiscale…

Numerical Analysis · Computer Science 2015-06-19 S. Karimi , K. B. Nakshatrala

The present article proposes a partitioned Dirichlet-Neumann algorithm, that allows to address unique challenges arising from a novel mixed-dimensional coupling of very slender fibers embedded in fluid flow using a regularized mortar-type…

Numerical Analysis · Mathematics 2023-12-04 Nora Hagmeyer , Matthias Mayr , Alexander Popp

This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a…

Numerical Analysis · Mathematics 2024-10-08 Christopher R. Wentland , Francesco Rizzi , Joshua Barnett , Irina Tezaur

We present a numerical scheme for the solution of nonlinear mixed-dimensional PDEs describing coupled processes in embedded tubular network system in exchange with a bulk domain. Such problems arise in various biological and technical…

Computational Engineering, Finance, and Science · Computer Science 2021-11-23 Timo Koch , Hanchuan Wu , Martin Schneider

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

Machine Learning · Statistics 2021-08-23 Patrick Héas , Cédric Herzet

Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier-Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Model reduction allows…

Computational Physics · Physics 2019-08-07 Kilian Weishaupt , Alexandros Terzis , Ioannis Zarikos , Guang Yang , Matthijs de Winter , Rainer Helmig

A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time…

Numerical Analysis · Mathematics 2018-09-26 Gurpreet Singh , Mary F. Wheeler

This paper makes the first attempt to apply newly developed upwind GFDM for the meshless solution of two-phase porous flow equations. In the presented method, node cloud is used to flexibly discretize the computational domain, instead of…

Numerical Analysis · Mathematics 2022-04-19 Xiang Rao , Yina Liu , Hui Zhao

Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…

Numerical Analysis · Mathematics 2025-04-25 Valentina Schüller , Philipp Birken , Andreas Dedner

In this paper, we extend the reinterpreted discrete fracture model for flow simulation of fractured porous media containing flow blocking barriers on non-conforming meshes. The methodology of the approach is to modify the traditional…

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

The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as…

In this paper, a novel meshless method that can handle porous flow problems with singular source terms is developed by virtually constructing the node control domains. By defining the connectable node cloud, this novel meshless method uses…

Numerical Analysis · Mathematics 2022-08-03 Xiang Rao

This paper focuses on a new framework for reduced order modelling of non-intrusive data with application to 2D flows. To overcome the shortcomings of intrusive model order reduction usually derived by combining the POD and the Galerkin…

Numerical Analysis · Mathematics 2016-11-16 D. A. Bistrian , I. M. Navon