This paper presents a finite particle approximation of the two-fluid model for liquid ⁴He using smoothed particle hydrodynamics (SPH). In recent years, several studies have combined the vortex filament model (VFM), which describes quantized vortices in superfluid components, with the Navier–Stokes equations, which describe the motion of normal fluids. These studies led us to assume that coupling both components of the two-fluid model instead of using the VFM to describe the superfluid component enables us to approximate the system. In this study, we formulated a new SPH model that simultaneously solves both equations of motion of the two-fluid model. We then performed a numerical simulation of the rotating liquid ⁴He using our SPH. The results showed that the two major phenomena, the emergence of multiple independent vortices parallel to the circular axis and that of the so-called rigid-body rotation, can be reproduced by solving the two-fluid model using SPH. This finding is interesting because it was previously assumed that only a single vortex emerges when addressing similar problems without considering quantum mechanics. Our further analysis found that the emergence of multiple independent vortices can be realized by reformulating the viscosity term of the two-fluid model to conserve the angular momentum of the particles around their axes. Consequently, our model succeeded in reproducing the phenomena observed in quantum cases, even though we solve the phenomenological governing equations of liquid ⁴He.

本文使用平滑粒子流体动力学 (SPH)提出了液体⁴ He的双流体模型的有限粒子近似。近年来，一些研究将描述超流体成分中的量化涡旋的涡旋丝模型 (VFM) 与描述正常流体运动的 Navier-Stokes 方程相结合。这些研究使我们假设耦合双流体模型的两个组件而不是使用 VFM 来描述超流体组件使我们能够近似系统。在这项研究中，我们制定了一个新的 SPH 模型，它可以同时求解双流体模型的两个运动方程。然后我们对旋转液体进行了数值模拟⁴他使用我们的 SPH。结果表明，两个主要现象，平行于圆轴的多个独立涡的出现和所谓的刚体旋转，可以通过使用SPH求解双流体模型来重现。这一发现很有趣，因为之前假设在不考虑量子力学的情况下解决类似问题时只会出现一个漩涡。我们的进一步分析发现，通过重新制定双流体模型的粘度项以守恒粒子绕其轴的角动量，可以实现多个独立涡旋的出现。因此，我们的模型成功地再现了在量子情况下观察到的现象，即使我们求解了液体⁴ He的现象学控制方程。