A weakly compressible hybridizable discontinuous Galerkin formulation for fluid–structure interaction problems

Andrea La Spina, Martin Kronbichler, Matteo Giacomini, Wolfgang A. Wall, Antonio Huerta

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


A scheme for the solution of fluid–structure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid equations, while the standard continuous Galerkin (CG) approach is adopted for the structural problem. The chosen HDG solver combines robustness of discontinuous Galerkin (DG) approaches in advection-dominated flows with higher-order accuracy and efficient implementations. Two coupling strategies are examined in this contribution, namely a partitioned Dirichlet–Neumann scheme in the context of hybrid HDG–CG discretizations and a monolithic approach based on Nitsche's method, exploiting the definition of the numerical flux and the trace of the solution to impose the coupling conditions. Numerical experiments show optimal convergence of the HDG and CG primal and mixed variables and superconvergence of the postprocessed fluid velocity. The robustness and the efficiency of the proposed weakly compressible formulation, in comparison to a fully incompressible one, are also highlighted on a selection of two and three dimensional FSI benchmark problems.

Original languageEnglish
Article number113392
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - 1 Dec 2020


  • Finite elements
  • Fluid–structure interaction
  • Hybridizable discontinuous Galerkin
  • Navier–Stokes equations
  • Nitsche's method
  • Weakly compressible flows


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