{"paper":{"title":"Stochastic Galerkin finite volume shallow flow model: well-balanced treatment over uncertain topography","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Georges Kesserwani, James Shaw","submitted_at":"2019-07-15T10:37:12Z","abstract_excerpt":"Stochastic Galerkin methods can quantify uncertainty at a fraction of the computational expense of conventional Monte Carlo techniques, but such methods have rarely been studied for modelling shallow water flows. Existing stochastic shallow flow models are not well-balanced and their assessment has been limited to stochastic flows with smooth probability distributions. This paper addresses these limitations by formulating a one-dimensional stochastic Galerkin shallow flow model using a low-order Wiener-Hermite Polynomial Chaos expansion with a finite volume Godunov-type approach, incorporating"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06421","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"}