When numerically computing high Reynolds number cavity flow, it is known that by formulating the Navier-Stokes equations using the stream function and vorticity as unknown functions, it is possible to reproduce finer flow structures. Although numerical computations applying methods such as the finite difference method are well known, to the best of our knowledge, there are no examples of applying particle-based methods like the SPH method to this problem. Therefore, we applied the SPH method to the Navier-Stokes equations, formulated with the stream function and vorticity as unknown functions, and conducted numerical computations of high Reynolds number cavity flow. The results confirmed the reproduction of small vortices and demonstrated the effectiveness of the scheme using the stream function and vorticity.

翻译：在高雷诺数空腔流的数值计算中，已知通过将纳维-斯托克斯方程以流函数和涡量作为未知函数进行公式化，能够再现更精细的流动结构。虽然应用有限差分法等方法的数值计算已广为人知，但据我们所知，目前尚未有将SPH等基于粒子的方法应用于此问题的先例。因此，我们将SPH方法应用于以流函数和涡量为未知函数公式化的纳维-斯托克斯方程，并对高雷诺数空腔流进行了数值计算。结果证实了微小涡旋的再现，并验证了采用流函数与涡量方案的有效性。