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Related papers: Dynamic phase-field fracture with a first-order di…

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Many geo-engineering applications, e.g., enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field…

Geophysics · Physics 2023-04-27 Fan Fei , Andre Costa , John E. Dolbow , Randolph R. Settgast , Matteo Cusini

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…

Computational Physics · Physics 2015-04-22 Sebastian Acosta , Charles Puelz , Beatrice Riviere , Daniel J. Penny , Craig G. Rusin

We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions.…

Applied Physics · Physics 2019-03-27 Rudy J. M. Geelen , Yingjie Liu , Tianchen Hu , Michael R. Tupek , John E. Dolbow

We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and…

Numerical Analysis · Mathematics 2023-06-28 Stefano Bonetti , Michele Botti , Ilario Mazzieri , Paola F. Antonietti

This paper presents a high-order discontinuous Galerkin (DG) scheme for the simulation of wave propagation through coupled elastic-acoustic media. We use a first-order stress-velocity formulation, and derive a simple upwind-like numerical…

Numerical Analysis · Mathematics 2020-07-15 Kaihang Guo , Sebastian Acosta , Jesse Chan

In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…

Numerical Analysis · Mathematics 2015-07-29 Leilei Wei

Recently, the phase field method has been increasingly used for brittle fractures in soft materials like polymers, elastomers, and biological tissues. When considering finite deformations to account for the highly deformable nature of soft…

Materials Science · Physics 2024-08-22 S. Mohammad Mousavi , Ida Ang , Jason Mulderrig , Nikolaos Bouklas

Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We…

Materials Science · Physics 2015-05-18 R. Spatschek , E. Brener , A. Karma

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities, and multi-physics…

A discontinuous Galerkin method has been developed for strain gradient-dependent damage. The strength of this method lies in the fact that it allows the use of $C^0$ interpolation functions for continuum theories involving higher-order…

Computational Physics · Physics 2009-09-29 L. Molari , G. N. Wells , K. Garikipati , F. Ubertini

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

Numerical Analysis · Mathematics 2020-01-08 Hong Xiao , Eky Febrianto , Qiaoling Zhang , Fehmi Cirak

Discrete fracture models with reduced-dimensional treatment of conductive and blocking fractures are widely used to simulate fluid flow in fractured porous media. Among these, numerical methods based on interface models are intensively…

Numerical Analysis · Mathematics 2024-05-14 Yong Liu , Ziyao Xu

4D acoustic imaging via an array of 32 sources / 32 receivers is used to monitor hydraulic fracture propagating in a 250~mm cubic specimen under a true-triaxial state of stress. We present a method based on the arrivals of diffracted waves…

Geophysics · Physics 2020-06-22 Dong Liu , Brice Lecampion , Thomas Blum

This paper presents and analyzes a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media. We use a first order time extrapolation which allows us to solve the equations implicitly and sequentially. We…

Numerical Analysis · Mathematics 2022-01-12 Giselle Sosa Jones , Beatrice Riviere , Loic Cappanera

The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by…

Numerical Analysis · Mathematics 2021-04-14 Paola F. Antonietti , Michele Botti , Ilario Mazzieri , Simone Nati Poltri

In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite…

Numerical Analysis · Mathematics 2024-04-10 Satyajith Bommana Boyana , Thomas Lewis , Sijing Liu , Yi Zhang

We present a scalable 2D Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo-impulsive formulation of the problem is solved in…

Numerical Analysis · Mathematics 2023-02-22 Jens Visbech , Allan P. Engsig-Karup , Harry B. Bingham

This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a…

Numerical Analysis · Mathematics 2020-02-19 Mats Kirkesæther Brun , Thomas Wick , Inga Berre , Jan Martin Nordbotten , Florin Adrian Radu

In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the…

Numerical Analysis · Mathematics 2021-12-06 Paola F. Antonietti , Ilario Mazzieri , Francesco Migliorini

An energy-based discontinuous Galerkin method for the advective wave equation is proposed and analyzed. Energy-conserving or energy-dissipating methods follow from simple, mesh-independent choices of the inter-element fluxes, and both…

Numerical Analysis · Mathematics 2019-03-19 Lu Zhang , Thomas Hagstrom , Daniel Appelo