Parallel Block Adaptive Mesh Refinement For Multiphase Flows

1. Parallel Block Adaptive Mesh Refinement For Multiphase Flows D. Zuzio* J-L. Estivalezes* *ONERA/DMAE, 2 av. Édouard Belin, 31055 Toulouse, France Context • Background: • Study of complex interfacial flows • Example: Atomization of fuel in combustion chambers • Objectives: • Realization of DNS simulations • Perform parallel computations • Use of adaptive mesh refinement to allow high • resolutions The study of liquid-gas interactions have a fundamental importance, especially in combustion problems. The interfacial instabilities, like the Kelvin-Helmholtz, produce the droplets or sprays that afterwards participate to combustion. In particular where experiments are too difficult or expensive to perform, the numerical simulation becomes a powerful tool for predicting these physical phenomena. The direct numerical simulation (DNS) gives a "model free" approach to the Navier Stokes equations, at the price, however, of a higher computational resources demand. Experimental study of the disintegration of a liquid sheet, H. Carentz, ONERA Numerical method - AMR • PARAMESH* package • Quad-tree block type AMR • Parallel workload balance • Coarse-fine interface managing • Allows multigrid • Resolution of Navier Stokes equations • Resolution in each fluid • Incompressible flows hypothesis • Explicit projection method • Interface tracking • Two non-miscible fluids • Level-Set method • Immediate knowledge of interface • position and geometry • Jump conditions • Ghost-Fluid method • Jumps always evaluated • on the finest mesh • Adaptive Mesh Refinement • “Near interface” refinement criterion: • the mesh refines automatically when the proximity of the interface is detected * http://www.physics.drexel.edu/~olson/paramesh-doc/Users_manual/amr.html Elliptic solver Results • BiCG-Stab • Strong density ratio flows • Unsymmetrical linear systems • Local block matrix strategy • Preconditioning • FAC multigrid preconditioner • Use of tree blocks for multigrid • Fast Adaptive Composite grid algorithm l0 l1 l2 l3 Use of AMR tree for multigrid preconditioner Simulation of a Rayleigh-Taylor instability with five levels of adaptive mesh Bibliography Kevin Olson. Paramesh: A parallel adaptive grid tool. in Parallel Computational Fluid Dynamics 2005: Theory and Applications: Proceedings of the Parallel CFD Conference, College Park, MD, U.S.A., eds. A. Deane, A. Ecer, G. Brenner, D. Emerson, J. McDonough, J. Periaux, N. Satofuka, and D. Tromeur-Dervout (Elsevier), 2006. M. Sussman. A parallelized, adaptive algorithm for multiphase flows in general geometries. Computers and Structures, 2005. R. Teigland and I. K. Eliassen. A multiblock/multilevel mesh refinement procedure for cfd computations. International journal for numerical methods in fluids, 2001. H. A. VanDerVorst. Bi-CGstab: a fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems. SIAM Journal of Scientific Computing, 1992,11. Conclusions & Perspectives A global second order explicit projection method for incompressible two phase flows has been improved with parallel adaptive mesh refinement. The ability to perform high density ratio computations has been demonstrated, in particular the capability of the elliptic solver to converge for all the test cases. With local interface refinement an AMR simulation can nearly achieve the fine grid precision, thus allowing great computational resources saving. Acknowledgements This research project has been supported by a Marie Curie Early Stage Research Training Fellowship of the European Community Sixth Framework Program under contract number MEST-CT-2005-020426.