{"paper":{"title":"Particle velocity based universal algorithm for numerical simulation of hydraulic fractures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","physics.geo-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Gennady Mishuris, Michal Wrobel","submitted_at":"2014-12-15T22:22:34Z","abstract_excerpt":"In the paper, we propose a new effective mathematical formulation and resulting universal numerical algorithm capable of tackling various HF models in the framework of a unified approach. The presented numerical scheme is not limited to any particular elasticity model or crack propagation regime. Its basic assumptions are: i) proper choice of independent and dependent variables (with the direct utilization of a new one - the reduced particle velocity), ii) tracing the fracture front by use of the speed equation which can be integrated in a closed form and sets an explicit relation between the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5529","kind":"arxiv","version":3},"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"}