{"paper":{"title":"Variable Smoothing Lengths and Energy Conservation in Smoothed Particle Hydrodynamics","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"John C.B. Papaloizou, Richard P. Nelson","submitted_at":"1994-06-17T15:56:26Z","abstract_excerpt":"We present a new formulation of the equations of motion used in smoothed particle hydrodynamics (SPH). The spatial resolution in SPH is determined by the smoothing length, $h$, and it has become common practice for each particle to be given its own adaptive smoothing length, $h_i$. Consequently, the dynamic range that may be spatially resolved is greatly increased, but additional ($\\nabla h$) terms, which account for the variability of the smoothing lengths, should appear in the equations of motion in order to satisy conservation requirements. Previous implementations of SPH have neglected the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9406053","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}