{"paper":{"title":"A Godunov Method for Multidimensional Radiation Magnetohydrodynamics based on a variable Eddington tensor","arxiv_id":"1201.2223","primary_cat":"astro-ph.HE","submitted_at":"2012-01-11T02:25:34+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":0.88,"id":"s0","own":true,"role":"contribution","text":"We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.92,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.12,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.88,"interpretation":0.0}},{"i":1,"p":0.93,"id":"s1","own":true,"role":"method","text":"This algorithm solves the radiation moment equations in the mixed frame, without invoking any diffusion-like approximations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.84,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.93,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.07,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"method","text":"The moment equations are closed using a variable Eddington tensor whose components are calculated from a formal solution of the transfer equation at a large number of angles using the method of short characteristics.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":1.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.74,"id":"s3","own":true,"role":"method","text":"We use a comprehensive test suite to verify the algorithm, including convergence tests of radiation-modified linear acoustic and magnetosonic waves, the structure of radiation modified shocks, and two-dimensional tests of photon bubble instability and the ablation of dense clouds by an intense radiation field.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.96,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.49,"role_probabilities":{"gap":0.0,"method":0.74,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.24,"interpretation":0.0}},{"i":4,"p":0.58,"id":"s4","own":true,"role":"method","text":"These tests cover a very wide range of regimes, including both optically thick and thin flows, and ratios of the radiation to gas pressure of at least 10^{-4} to 10^{4}.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.85,"main_claim_p":0.07,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.58,"result":0.11,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.31,"interpretation":0.0}},{"i":5,"p":0.99,"id":"s5","own":true,"role":"result","text":"Across most of the parameter space, we find the method is accurate.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.38,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.01}},{"i":6,"p":0.99,"id":"s6","own":true,"role":"limitation","text":"However, the tests also reveal there are regimes where the method needs improvement, for example when both the radiation pressure and absorption opacity are very large.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.95,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.01,"background":0.0,"limitation":0.99,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":7,"p":0.94,"id":"s7","own":true,"role":"future_work","text":"We suggest modifications to the algorithm that will improve accuracy in this case.","hedge":{"p":0.94,"label":"hedged_possibility"},"own_p":0.64,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.0,"limitation":0.02,"future_work":0.94,"contribution":0.03,"interpretation":0.0}},{"i":8,"p":0.72,"id":"s8","own":true,"role":"interpretation","text":"We discuss the advantages of this method over those based on flux-limited diffusion.","hedge":{"p":0.61,"label":"asserted"},"own_p":0.54,"main_claim_p":0.09,"quantitative":true,"quantitative_p":0.63,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.1,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.17,"interpretation":0.72}},{"i":9,"p":0.76,"id":"s9","own":true,"role":"result","text":"In particular, we find the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.93,"main_claim_p":0.36,"quantitative":true,"quantitative_p":0.92,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.76,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.23}}]},"compiled":{"main_claim":{"p":0.7,"text":"In particular, we find the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.","location":"abstract s9","hedge_strength":{"p":0.99,"label":"asserted"}},"provenance":{"route":{"via":"OpenRouter","model":"classifier-1.13","endpoint":"https://openrouter.ai/api/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":7552,"cost_usd_reported":0.000317},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.03,"states_limitation":0.98,"human_participants":0.01,"controlled_comparison":0.2,"randomized_assignment":0.01,"states_quantitative_result":0.93,"compares_with_prior_results":0.91,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":1.0,"value":"simulation or computation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":0.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":1.0}},"contribution_type":{"p":1.0,"value":"method or tool","probabilities":{"review":0.0,"method_or_tool":1.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.0,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.95,"text":"We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods.","location":"abstract s0"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":10,"sentences_in_abstract":10},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}