273 IGPM.pdf        February 2007
TITLE Numerical Simulation of Cavitation Bubbles by Compressible Two-Phase Fluids
AUTHORS Siegfried Müller, Philippe Helluy, Josef Ballmann
ABSTRACT The present work deals with the numerical investigation of collapsing cavitation bubbles in compressible Here the of a two-phase vapor-liquid mixture is modeled by a single compressible medium. This is characterized by the stiffened gas law using different material parameters for the two phases. For the discretization of the stiffened gas model the approach of Abgrall and Saurel is employed where the equations, here the Euler equations, for the conserved quantities are approximated by a finite volume scheme and an upwind discretization is used for the non-conservative transport equations of the pressure law coefficients. The original 1st order discretization is extended to higher order applying 2nd order ENO reconstruction to the primitive variables. The derivation of the nonconservative upwind discretization for the phase indicator, here the gas fraction, is presented for arbitrary unstructured grids. The efficiency of the numerical scheme is significantly improved by employing local grid adaptation. For this purpose multiscale-based grid adaptation is used in combination with a multilevel time stepping strategy to avoid small time steps for coarse cells. The resulting numerical scheme is then applied to the numerical investigation of the collapse of a vapor bubble in a free field and near to a rigid wall.
KEYWORDS
DOI 10.1002/fld.2033
PUBLICATION Int. Journal for Numerical Methods in Fluids
Volume 62, Issue 6, 591-631 (2010)

Oberwolfach reports
OWR 11/2008, 33-35 (2008)