Parallel Block Adaptive Mesh Refinement For Multiphase Flows

D. Zuzio*J-L. Estivalezes*

*ONERA/DMAE, 2 av. Édouard Belin, 31055 Toulouse, France

Simulation of a Rayleigh-Taylor instability with five levels of adaptive mesh

Elliptic solver

Numerical method - AMR

Context

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.

BibliographyKevin 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 & PerspectivesA 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.AcknowledgementsThis 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.

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

* http://www.physics.drexel.edu/~olson/paramesh-doc/Users_manual/amr.html

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

Results

Adaptive Mesh Refinement “Near interface” refinement criterion:

the mesh refines automatically when the

proximity of the interface is detected

Experimental study of the disintegration of a liquid sheet, H. Carentz, ONERA

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

Rebyax

e222

22)()(

numericalanaliticalerr

l0 l1 l2 l3Use of AMR tree for multigrid preconditioner