Parallel computations of droplet oscillations

液滴振動の並列計算

渡辺 正

Watanabe, Tadashi

浮遊液滴は容器壁の影響を受けないため、高温の溶融金属の物性測定に利用することができ、液滴形状振動の振動数及び減衰から、線形理論に基づき表面張力と粘性がそれぞれ求められる。液滴形状の変形が大きい場合、非線形効果が顕著になり、また内部流動の影響が懸念される。本報告では、液滴の3次元振動挙動を数値シミュレーションにより調べ、振動振幅が振動周波数へ及ぼす影響を検討した結果について示す。シミュレーションにおいては、圧力方程式の解法として共役勾配法を用い、並列化により48台で32倍から48倍の高速化を達成した。行列計算部分のみに関しては、48倍から68倍であった。並列化の際に必要となる前処理行列として点ヤコビ法,ブロックヤコビ法,加法シュワルツ法を比較し、液滴シミュレーション時のそれぞれの特性と高速化の関連について検討した。さらに、並列計算時のデータ転送速度の影響等についても検討した結果を示す。

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.