Accuracy Improvements for Single Precision Implementations of the SPH Method

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.