Parallel computations of droplet oscillations

Watanabe, Tadashi

A levitated liquid droplet is used to measure material properties of molten metal at high temperature, since the levitated droplet is not in contact with a container, and the effect of the container wall is eliminated for a precise measurement. Viscosity and surface tension are, respectively, obtained from the damping and the frequency of an oscillation of the droplet shape. Large-amplitude oscillations are desirable from the viewpoint of measurement. However, the relation between material properties and oscillation parameters, which is generally used to calculate material properties, is based on the linear theory given by Lamb, and small-amplitude oscillations are necessary for an estimation of material properties. In this study, numerical simulations of an oscillating liquid droplet are performed to study the effect of the amplitude on the oscillation frequency of the droplet. Three-dimensional Navier-Stokes equations are solved using the level set method, and it is shown that the oscillation frequency becomes small as the amplitude increases. The Poisson equation is solved using the Bi-CGSTAB method. The domain decomposition technique is applied and the message passing interface (MPI) library is used for parallel computations. Three preconditioners are compared for the Bi-CGSTAB method; the point Jacobi (PJ), block Jacobi (BJ), and overlapping additive Schwarz (AS) schemes. It is shown that the speedup of the PJ scheme is larger than that of the BJ and AS schemes, and the BJ scheme is almost the same as the AS scheme. The effect of cache is notable for the PJ scheme. The BJ and AS schemes are found to be better when the number of processors is small.