One of the main issues with naive Smoothed Particle Hydrodynamics (SPH) implementations is the lack of uniform accuracy in the computational domain. If not mastered correctly, this leads to non-physical predictions when dealing with large-domain hydraulic problems or with very fine resolutions. The present article addresses two recommended methodologies to achieve the best numerical accuracy with single-precision SPH implementations, using the GPUSPH engine as reference. A still water test case is examined using different approaches. Instead of operating with the physical particle positions, the use of positions relative to the neighbour-search grid leads to a homogeneous accuracy distribution throughout the domain, with a consequent improvement in energy conservation. Further improvements are attained by evolving the relative density variation in the fluid equations, instead of the physical density. This helps in bounding the numerical errors within the machine epsilon and prevents any spurious behaviour due to error accumulation.

中文翻译：

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SPH 方法单精度实现的精度改进

朴素平滑粒子流体动力学 (SPH) 实现的主要问题之一是计算域中缺乏统一的精度。如果没有正确掌握，这会导致在处理大域水力问题或非常精细的分辨率时进行非物理预测。本文使用 GPUSPH 引擎作为参考，介绍了两种推荐的方法，以通过单精度 SPH 实现实现最佳数值精度。使用不同的方法检查静水测试案例。不是使用物理粒子位置操作，而是使用相对于邻域搜索网格的位置导致整个域的均匀精度分布，从而提高能量守恒。通过发展流体方程中的相对密度变化而不是物理密度，可以获得进一步的改进。这有助于限制机器 epsilon 内的数值误差，并防止由于误差累积而导致的任何虚假行为。