{"paper":{"title":"A general approach to enhance slope limiters on non-uniform rectilinear grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Xianyi Zeng","submitted_at":"2013-01-06T03:12:38Z","abstract_excerpt":"Most slope limiter functions in high-resolution finite volume methods to solve hyperbolic conservation laws are designed assuming one-dimensional uniform grids, and they are also used to compute slope limiters in computations on non-uniform rectilinear grids. However, this strategy may lead to either loss of total variation diminishing (TVD) stability for 1D linear problems or the loss of formal second-order accuracy if the grid is highly non-uniform. This is especially true when the limiter function is not piecewise linear. Numerical evidences are provided to support this argument for two pop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0967","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"}