Finite element method for incompressible viscous flow with immersed pressure jumps with applications to actuator disks and microfluidics

  • Roberto AusasEmail author
  • Gustavo Buscaglia
  • Vitoriano Ruas
Technical Paper


We propose a finite element method for the solution of viscous incompressible flow problems with singular forces at immersed interfaces. The method combines the algebraic subgrid scale method with a pressure jump stabilization. It consists of the addition, to the continuity equation, of a term weighting the residual of the pressure jump. This term enhances the stability irrespective of possible badly shaped intersections of the interface with the finite elements. We assess the new method by comparing with the unstabilized case showing improved accuracy and robustness. The examples consider immersed actuator disk problems and one application to thermocapillary convection.


Finite elements Incompressible viscous flows Navier–Stokes Pressure jump Immersed boundary Surface tension 



The authors gratefully acknowledge the financial support received from both FAPESP (Grants 2014/19249-1, 2013/07375-0-Cepid-CeMEAI) and CNPq (Grants 307996/2008-5, 447607/2014-6 and 308728/2013-0).


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrazil
  2. 2.Sorbonne Université, UMR 7190, CNRSInstitut Jean Le Rond d’AlembertParisFrance
  3. 3.Department of Mechanical EngineeringCNPq Research grant holder, PUC-RioRio de JaneiroBrazil

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