Hourglass Control for the Stabilized Finite Element Solution of Coupled Incompressible Viscous Flows and Heat Transfer
André L. Rossa, José J. Camata, Alvaro L. G. A. Coutinho
This work presents an implementation of a stabilized ﬁnite element formulation for incompressible viscous ﬂow coupled with the advective-diffusive temperature transport equation through the Boussinesq approximation approach. For solving of the incompressible Navier-Stokes equations we use the Streamline Upwind Petrov-Galerkin/Pressure Stabilized Petrov-Galerkin (SUPG/PSPG) formulation and for the advective transport equation the SUPG formulation is employed. A comparison of the computational performance between full Gaussian and reduced (centre of the element) integrations for the isoparametric 8-node hexahedron element is presented. A h-stabilization for both advective and viscous/diffusive terms is used to control the spurious hourglass modes introduced by under integrating the element. The implementation has been performed using the libMesh Finite Element Method (FEM) library (http://libmesh.sourceforge.net) which provides support for adaptive mesh reﬁnement and coarsening (AMR/C) and parallel computations. A veriﬁcation is made using the Kim-Moin problem and the computational performance is evaluated solving a natural convection problem in a parallel machine.
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