In this paper we propose a dual-time stepping scheme for the Smoothed Particle Hydrodynamics (SPH) method. Dual-time stepping has been used in the context of other numerical methods for the simulation of incompressible fluid flows. Here we provide a scheme that combines the entropically damped artificial compressibility (EDAC) along with dual-time stepping. The method is accurate, robust, and demonstrates up to seven times better performance than the standard weakly-compressible formulation. We demonstrate several benchmarks showing the applicability of the scheme. In addition, we provide a completely open source implementation and a reproducible manuscript.

在本文中，我们为平滑粒子流体动力学 (SPH) 方法提出了一种双时间步进方案。双时间步进已在其他数值方法的背景下用于不可压缩流体流动的模拟。在这里，我们提供了一种将熵阻尼人工可压缩性 (EDAC) 与双时间步进相结合的方案。该方法准确、稳健，并且表现出比标准弱可压缩公式高七倍的性能。我们展示了几个显示该方案适用性的基准。此外，我们还提供完全开源的实现和可复制的手稿。