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CivilComp Proceedings
ISSN 17593433 CCP: 91
PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping, L.F. Costa Neves and R.C. Barros
Paper 274
Distributed Parallel Computation of ThreeDimensional Incompressible Flows using an Implicit Monolithic Finite Element Formulation A.R.E. Antunes, R.S. Da Silva, P.R.M. Lyra and R.B. Willmersdorf
Department of Mechanical Engineering, Federal University of Pernambuco, Recife, Brazil A.R.E. Antunes, R.S. Da Silva, P.R.M. Lyra, R.B. Willmersdorf, "Distributed Parallel Computation of ThreeDimensional Incompressible Flows using an Implicit Monolithic Finite Element Formulation", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 274, 2009. doi:10.4203/ccp.91.274
Keywords: finite element modelling, incompressible NavierStokes, edge based data structure, fractionalstep method, parallel computing.
Summary
The objective of this paper is to present a computational system capable of numerically simulating threedimensional laminar incompressible NavierStokes fluid flow problems written in primitive variable form, using parallel computing. A formulation using a stabilized finite element method and fractional step method is adopted, and a second order stable monolithic formulation is obtained [1,2,3]. An edgebased data structure is used. The main advantage of this data structure is the reduction of the computational time necessary for simulations as all coefficients are calculated in a preprocessing step. The local conservation and symmetry are enforced at the discrete level calculating only the nondiagonal terms and by computing the diagonal one as the negative value of the summation of the samerow nondiagonal terms. The final edge based terms are obtained replacing the standard loop over the elements by edge loops. This formulation has stability properties for the pressure and advective terms based on their projections in the finite element spaces. The parallel communication is managed using the MPI (Message Passing Interface). The domain decomposition is obtained using the ParMetis (Parallel Graph Partitioning and Fillreducing Matrix Ordering) and the distributed arrays and the final algebraic system of equations uses the PETSc (Portable, Extensible Toolkit for Scientific Computation) toolkit. The computational program developed was verified using several model problems and the results obtained are in agreement with the experimental, theoretical and numerical data available in the literature for laminar fluid flow. A preliminary performance study was completed and good speedup was obtained. Further studies are required for exploiting the whole system capacity and to properly verify the computational efficiency of the parallel program.
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