 A phase field approach to pressurized fractures using discontinuous Galerkin methodsChristian Engwer and Liesel Schumacher Mathematics and Computers in Simulation (MATCOM), 2017, vol. 137, issue C, 266-285 Abstract: Subsurface fractures play an important role in many modern energy technologies (e.g. geothermal energy, fracking, nuclear waste management). Real world experiments concerning fracture propagation are usually expensive and time consuming, therefore numerical simulations become more and more important in this area. The main challenge for numerical methods is the evolving domain. Standard finite element (FE) methods require remeshing to resolve the crack surface once a fracture starts propagating. To overcome this problem we use a phase field approach to regularize the crack surface. Thereby we consider quasi static evolution in fluid filled media. For the one-dimensional case Γ-convergence of the approximating functional to the potential energy of the system is shown. Based on this model we propose a discontinuous Galerkin (DG) formulation for the displacement. This takes into account displacement jumps at the crack surface. Numerical experiments compare our method with a standard FE approach. Keywords: Fracture propagation; Phase field; Gamma convergence; Discontinuous Galerkin (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:137:y:2017:i:c:p:266-285 DOI: 10.1016/j.matcom.2016.11.001 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.