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Required storage precision per SPH particle attribute

Determine the storage precision required for each Smoothed Particle Hydrodynamics (SPH) particle attribute to maintain accuracy and stability, identifying which fields must be stored in double precision and which can use reduced mantissa widths.

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Background

SPH simulations involve many floating-point quantities with differing sensitivity to precision. While positions and densities may need higher accuracy, other fields (e.g., smoothing length) may tolerate reduced precision.

The authors explicitly state uncertainty about precision requirements per field and provide empirical indications, but call for a systematic determination of precision needs.

References

It is not clear in which precision different fields have to be stored: Even if we assume that double precision is required for primary, physical quantities, properties such as the smoothing length carry a lower information density: A difference in h in the order of floating-point accuracy most often does not include more particles into the underlying truncated sum, while even additional particles do not affect the algorithm outcome negatively.

— An extension of C++ with memory-centric specifications for HPC to reduce memory footprints and streamline MPI development (2406.06095 - Radtke et al., 10 Jun 2024) in Section 5.4 (Floating point accuracy)