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