{"paper":{"title":"Mathematical modeling of thermal stabilization of vertical wells on high performance computing systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CE","authors_text":"Maria V. Vasilyeva, Natalia V. Pavlova, Petr N. Vabishchevich","submitted_at":"2013-04-05T07:13:58Z","abstract_excerpt":"Temperature stabilization of oil and gas wells is used to ensure stability and prevent deformation of a subgrade estuary zone. In this work, we consider the numerical simulation of thermal stabilization using vertical seasonal freezing columns.\n  A mathematical model of such problems is described by a time-dependent temperature equation with phase transitions from water to ice. The resulting equation is a standard nonlinear parabolic equation.\n  Numerical implementation is based on the finite element method using the package Fenics. After standard purely implicit approximation in time and simp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1625","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"}