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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 27
TRENDS IN PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING Edited by: P. Iványi, B.H.V. Topping
Chapter 9
Scalable Hybrid Algorithms for LargeScale Parallel Computational Fluid Dynamics Applications S. Aliabadi, E. Yilmaz, M. Akbar, S. Palle, B. Soni and R. Patel
Northrop Grumman Center for High Performance Computing, Jackson State University, Jackson MS, United States of America S. Aliabadi, E. Yilmaz, M. Akbar, S. Palle, B. Soni, R. Patel, "Scalable Hybrid Algorithms for LargeScale Parallel Computational Fluid Dynamics Applications", in P. Iványi, B.H.V. Topping, (Editors), "Trends in Parallel, Distributed, Grid and Cloud Computing for Engineering", SaxeCoburg Publications, Stirlingshire, UK, Chapter 9, pp 187220, 2011. doi:10.4203/csets.27.9
Keywords: finite element, finite volume, incompressible flows, heat transfer, twofluid flows, shallow water flow, GMRES.
Summary
In this chapter we present our implicit hybrid finite element/volume solvers for threedimensional incompressible flows coupled with energy equation, threedimensional two immiscible fluids free surface flows, and twodimensional shallow water flows. Our general approach is to solve the Navier Stokes equations using the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrixfree implicit cellcentered finite volume method. Then a pressure Poisson equation is solved by the nodebased Galerkin finite element method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field.
The incompressible flows we present here are governed by the NavierStokes equations with the Boussinesq buoyancy approximation coupled to the thermal energy transport equation. For turbulence we have incorporated the detached eddy simulation (DES) turbulence model to compute the eddy viscosity. The finite volume method is used for both temperature and eddy viscosities. For the twofluid freesurface flow solver, the fluidinterface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrixfree finite volume method as the one used for momentum equations is used to solve the advection equation. We use the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm which enforces the conservation of the mass for each fluid. In our hybrid shallow water flow solver, we solve the momentum equation using the cellcenter finite volume method and the wave continuity equation using nodebased finite element method. To enhance the stability of the hybrid method around discontinuities, we introduce a new shock capturing scheme which will act only around sharp interfaces without sacrificing the accuracy elsewhere. Several test problems are presented to demonstrate the robustness and applicability of our numerical methods. The parallelization is based on the Message Passing Interface (MPI) and our flow solvers are extremely well scalable on a parallel platform. purchase the fulltext of this chapter (price £20)
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