Particle methods for high-viscous free-surface flows are of great use to capture flow behaviors which are intermediate between solid and liquid. In general, it is important for numerical methods to satisfy the fundamental laws of physics such as the conservation laws of mass and momentum and the thermodynamic laws. Especially, the angular momentum conservation is necessary to calculate rotational motion of high-viscous objects. However, most of the particle methods do not satisfy the physical laws in their spatially discretized system. The angular momentum conservation law is broken mostly because of the viscosity models, which may result in physically strange behavior when high-viscous free-surface flow is calculated. In this study, a physically consistent particle method for high-viscous free-surface flows is developed. The present method was verified, and its performance was shown with calculating flow in a rotating circular pipe, high-viscous Taylor–Couette flow, and offset collision of a high-viscous object.

用于高粘度自由表面流动的粒子方法在捕获介于固体和液体之间的流动行为方面非常有用。通常，对于数值方法而言，重要的是要满足物理的基本定律，例如质量和动量的守恒定律以及热力学定律。特别地，角动量守恒对于计算高粘度物体的旋转运动是必要的。但是，大多数粒子方法在其空间离散系统中都不满足物理定律。角动量守恒定律主要是由于粘度模型而被打破的，当计算高粘度自由表面流时，这可能导致物理上奇怪的行为。在这项研究中，开发了一种用于高粘度自由表面流动的物理上一致的粒子方法。