{"paper":{"title":"Analysis of variable-step/non-autonomous artificial compression methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Michael McLaughlin, Robin Ming Chen, William Layton","submitted_at":"2018-09-12T20:04:41Z","abstract_excerpt":"A standard artificial compression (AC) method for incompressible flow is $$ \\frac{u_{n+1}^{\\varepsilon }-u_{n}^{\\varepsilon }}{k}+u_{n+1}^{\\varepsilon }\\cdot \\nabla u_{n+1}^{\\varepsilon }+{\\frac{1}{2}}u_{n+1}^{\\varepsilon }\\nabla \\cdot u_{n+1}^{\\varepsilon }+\\nabla p_{n+1}^{\\varepsilon }-\\nu \\Delta u_{n+1}^{\\varepsilon }=f\\text{ ,} \\\\ \\varepsilon \\frac{p_{n+1}^{\\varepsilon }-p_{n}^{\\varepsilon }}{k} +\\nabla \\cdot u_{n+1}^{\\varepsilon }=0 $$ for, typically, $\\varepsilon =k$ (timestep). It is fast, efficient and stable with accuracy $O(\\varepsilon +k)$. For adaptive (and thus variable) timestep "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04650","kind":"arxiv","version":2},"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"}