{"paper":{"title":"CRKSPH - A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme","arxiv_id":"1605.00725","primary_cat":"physics.comp-ph","submitted_at":"2016-05-03T01:38:16+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 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 v2","sentences":[{"i":0,"p":0.96,"id":"s0","own":true,"role":"contribution","text":"We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a first-order consistent reproducing kernel, a smoothing function that exactly interpolates linear fields with particle tracers.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.38,"role_probabilities":{"gap":0.0,"method":0.04,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.96,"interpretation":0.0}},{"i":1,"p":0.67,"id":"s1","own":false,"role":"background","text":"Previous formulations using reproducing kernel (RK) interpolation have had difficulties maintaining conservation of momentum due to the fact the RK kernels are not, in general, spatially symmetric.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.04,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":0.33,"method":0.0,"result":0.0,"background":0.67,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.88,"id":"s2","own":true,"role":"contribution","text":"Here, we utilize a reformulation of the fluid equations such that mass, linear momentum, and energy are all rigorously conserved without any assumption about kernel symmetries, while additionally maintaining approximate angular momentum conservation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.46,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":0.0,"method":0.11,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.88,"interpretation":0.0}},{"i":3,"p":0.59,"id":"s3","own":true,"role":"method","text":"Our approach starts from a rigorously consistent interpolation theory, where we derive the evolution equations to enforce the appropriate conservation properties, at the sacrifice of full consistency in the momentum equation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.59,"result":0.0,"background":0.0,"limitation":0.38,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":4,"p":0.61,"id":"s4","own":true,"role":"method","text":"Additionally, by exploiting the increased accuracy of the RK method's gradient, we formulate a simple limiter for the artificial viscosity that reduces the excess diffusion normally incurred by the ordinary SPH artificial viscosity.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.24,"role_probabilities":{"gap":0.0,"method":0.61,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.39,"interpretation":0.0}},{"i":5,"p":0.93,"id":"s5","own":true,"role":"contribution","text":"Collectively, we call our suite of modifications to the traditional SPH scheme Conservative Reproducing Kernel SPH, or CRKSPH.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.86,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.07,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.93,"interpretation":0.0}},{"i":6,"p":0.57,"id":"s6","own":true,"role":"contribution","text":"CRKSPH retains many benefits of traditional SPH methods (such as preserving Galilean invariance and manifest conservation of mass, momentum, and energy) while improving on many of the shortcomings of SPH, particularly the overly aggressive artificial viscosity and zeroth-order inaccuracy.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.66,"main_claim_p":0.53,"quantitative":true,"quantitative_p":0.67,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.04,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.57,"interpretation":0.38}},{"i":7,"p":0.64,"id":"s7","own":true,"role":"result","text":"We compare CRKSPH to two different modern SPH formulations (pressure based SPH and compatibly differenced SPH), demonstrating the advantages of our new formulation when modeling fluid mixing, strong shock, and adiabatic phenomena.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.45,"quantitative":true,"quantitative_p":0.66,"role_probabilities":{"gap":0.0,"method":0.13,"result":0.64,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.22,"interpretation":0.01}}]},"compiled":{"main_claim":{"p":0.5,"text":"CRKSPH retains many benefits of traditional SPH methods (such as preserving Galilean invariance and manifest conservation of mass, momentum, and energy) while improving on many of the shortcomings of SPH, particularly the overly aggressive artificial viscosity and zeroth-order inaccuracy.","location":"abstract s6","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":6542,"cost_usd_reported":0.0},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.06,"states_limitation":0.92,"human_participants":0.01,"controlled_comparison":0.6,"randomized_assignment":0.01,"states_quantitative_result":0.04,"compares_with_prior_results":0.97,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.88,"value":"simulation or computation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":0.12,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.88}},"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":0.66,"text":"We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a first-order consistent reproducing kernel, a smoothing function that exactly interpolates linear fields with particle tracers.","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 v2"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":8,"sentences_in_abstract":8},"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}}