eXtended Hybridizable Discontinuous Galerkin for incompressible flow problems with unfitted meshes and interfaces Articles uri icon

authors

publication date

  • February 2019

start page

  • 756

end page

  • 777

issue

  • 7

volume

  • 117

International Standard Serial Number (ISSN)

  • 0029-5981

Electronic International Standard Serial Number (EISSN)

  • 1097-0207

abstract

  • The eXtended hybridizable discontinuous Galerkin (X-HDG) method is developed for the solution of Stokes problems with void or material interfaces. X-HDG is a novel method that combines the hybridizable discontinuous Galerkin (HDG) method with an eXtended finite element strategy, resulting in a high-order, unfitted, superconvergent method, with an explicit definition of the interface geometry by means of a level-set function. For elements not cut by the interface, the standard HDG formulation is applied, whereas a modified weak form for the local problem is proposed for cut elements. Heaviside enrichment is considered on cut faces and in cut elements in the case of bimaterial problems. Two-dimensional numerical examples demonstrate that the applicability, accuracy, and superconvergence properties of HDG are inherited in X-HDG, with the freedom of computational meshes that do not fit the interfaces.

subjects

  • Aeronautics
  • Materials science and engineering
  • Mathematics

keywords

  • bimaterial; high-order; hybridizable discontinuous galerkin (hdg); interface; level-set; unfitted; void; x-fem; x-hdg