{"paper":{"title":"Constructing high-order discontinuity-capturing schemes with linear-weight polynomials and boundary variation diminishing algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Feng Xiao, Xi Deng, Yuya Shimizu","submitted_at":"2018-11-18T13:17:25Z","abstract_excerpt":"In this study, a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called $\\mathrm{P}_{n}\\mathrm{T}_{m}-\\mathrm{BVD}$ (polynomial of $n$-degree and THINC function of $m$-level reconstruction based on BVD algorithm), are designed by employing high-order linear-weight polynomials and THINC (Tangent of Hyperbola for INterface Capturing) functions with adaptive steepness as the reconstruction candidates. The final reconstruction function in each cell is determined with a multi-stage BVD (Boundary Variation Diminish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08316","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"}