{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T11:41:21Z","timestamp":1786534881117,"version":"3.56.0"},"reference-count":58,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T00:00:00Z","timestamp":1786492800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T00:00:00Z","timestamp":1786492800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["310833819"],"award-info":[{"award-number":["310833819"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["543332027"],"award-info":[{"award-number":["543332027"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["281466253"],"award-info":[{"award-number":["281466253"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In recent years, the Smoothed Particle Hydrodynamics (SPH) approach has been increasingly used for multiphase simulations involving interactions between diverse materials. A critical component of an SPH simulator is the pressure solver, which not only facilitates the simulation of compressible or incompressible fluids but also handles contact by preventing penetration between different materials. Currently, most SPH simulations in computer graphics employ implicit dual pressure solvers such as PBF, IISPH, or DFSPH. However, these solvers often exhibit instability when simulating high density ratios. Furthermore, they are difficult to strongly couple with many existing methods for non\u2010pressure forces, which typically utilize primal formulations. Consequently, pressure and non\u2010pressure solvers are often only weakly coupled, which can lead to stability issues. We present a novel implicit primal SPH pressure solver designed for multiphase simulations. Our method enables stable simulation of multiple interacting materials with large density ratios. We show that our solver robustly handles ratios of up to 1:1000 (e.g., air\u2010water interactions) which was not possible with previous implicit SPH pressure solvers. Moreover, we demonstrate how our solver allows for strong coupling with existing implicit simulation methods for viscosity, elasticity, and surface tension. Overall, our strong coupling significantly improves stability in complex multiphase simulations involving fluids, highly viscous materials, and deformable solids.<\/jats:p>","DOI":"10.1111\/cgf.70559","type":"journal-article","created":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T11:19:11Z","timestamp":1786533551000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Primal SPH Solver for Strongly Coupled Multiphase Simulations with High Density Ratios"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1908-4027","authenticated-orcid":false,"given":"Jan","family":"Bender","sequence":"first","affiliation":[{"name":"RWTH Aachen University  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3920-7765","authenticated-orcid":false,"given":"Stefan Rhys","family":"Jeske","sequence":"additional","affiliation":[{"name":"RWTH Aachen University  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-1024-6549","authenticated-orcid":false,"given":"Timna","family":"B\u00f6ttcher","sequence":"additional","affiliation":[{"name":"RWTH Aachen University  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6818-2953","authenticated-orcid":false,"given":"Fabian","family":"L\u00f6schner","sequence":"additional","affiliation":[{"name":"RWTH Aachen University  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,12]]},"reference":[{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508395"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/2766935"},{"key":"e_1_2_7_4_2","unstructured":"BenderJ. et al.:SPlisHSPlasH Library 2026. URL:https:\/\/github.com\/InteractiveComputerGraphics\/SPlisHSPlasH. 2 5 10"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/2159516.2159522"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/3730854"},{"key":"e_1_2_7_6_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/3730854. 2","DOI":"10.1145\/3730854"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1145\/3130800.3130854"},{"key":"e_1_2_7_8_2","unstructured":"BeckerM. IhmsenM. TeschnerM.: Corotated SPH for deformable solids. InProceedings of Eurographics Conference on Natural Phenomena(2009) pp.27\u201334. URL:https:\/\/dl.acm.org\/doi\/10.5555\/2381692.2381696. 3"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2016.2578335"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2020.3004245"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0045\u20107825(99)00051\u20101"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1017\/S1323358000018117"},{"key":"e_1_2_7_13_2","unstructured":"BeckerM. TeschnerM.: Weakly compressible SPH for free surface flows. InACM SIGGRAPH\/Eurographics Symposium on Computer Animation(2007) pp.1\u20138. URL:http:\/\/portal.acm.org\/citation.cfm?id=1272690.1272719. 2 3"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.2312\/vmv.20231244"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1145\/3763325"},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6118"},{"key":"e_1_2_7_17_2","doi-asserted-by":"crossref","unstructured":"DiazE. HsuJ. Montalvo\u2010RuizE. GilesC. YukselC.: Implicit Position\u2010Based Fluids. InProceedings of the SIGGRAPH Asia 2025 Conference Papers(Dec.2025). doi:10.1145\/3757377.3764005. 2","DOI":"10.1145\/3757377.3764005"},{"key":"e_1_2_7_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2025.113868"},{"key":"e_1_2_7_19_2","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392431"},{"key":"e_1_2_7_20_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.70082"},{"key":"e_1_2_7_21_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.70043"},{"key":"e_1_2_7_22_2","doi-asserted-by":"publisher","DOI":"10.1145\/2682630"},{"key":"e_1_2_7_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.110944"},{"key":"e_1_2_7_24_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2013.105"},{"key":"e_1_2_7_25_2","doi-asserted-by":"publisher","DOI":"10.2312\/egst.20141034"},{"key":"e_1_2_7_26_2","doi-asserted-by":"publisher","DOI":"10.1145\/3631936"},{"key":"e_1_2_7_27_2","doi-asserted-by":"publisher","DOI":"10.1145\/3480142"},{"key":"e_1_2_7_28_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14508"},{"key":"e_1_2_7_29_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14756"},{"key":"e_1_2_7_30_2","doi-asserted-by":"publisher","DOI":"10.2312\/vmv.20231245"},{"key":"e_1_2_7_31_2","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392400"},{"key":"e_1_2_7_32_2","doi-asserted-by":"publisher","DOI":"10.1145\/3649888"},{"key":"e_1_2_7_33_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2021.3055789"},{"key":"e_1_2_7_34_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14110"},{"key":"e_1_2_7_35_2","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530132"},{"key":"e_1_2_7_36_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14104"},{"key":"e_1_2_7_37_2","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461984"},{"key":"e_1_2_7_38_2","doi-asserted-by":"publisher","DOI":"10.1145\/2994258.2994272"},{"key":"e_1_2_7_39_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.astro.30.1.543"},{"key":"e_1_2_7_40_2","doi-asserted-by":"publisher","DOI":"10.1088\/0034\u20104885\/68\/8\/R01"},{"key":"e_1_2_7_41_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13317"},{"key":"e_1_2_7_42_2","doi-asserted-by":"publisher","DOI":"10.1145\/2766925"},{"key":"e_1_2_7_43_2","doi-asserted-by":"publisher","DOI":"10.1109\/tvcg.2016.2636144"},{"key":"e_1_2_7_44_2","doi-asserted-by":"publisher","DOI":"10.1145\/3708034"},{"key":"e_1_2_7_45_2","unstructured":"SolenthalerB. PajarolaR.: Density Contrast SPH Interfaces. InACM SIGGRAPH\/Eurographics Symposium on Computer Animation(2008) pp.211\u2013218. URL:http:\/\/dl.acm.org\/citation.cfm?id=1632592.1632623. 3 7"},{"key":"e_1_2_7_46_2","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531346"},{"key":"e_1_2_7_47_2","doi-asserted-by":"crossref","unstructured":"ShiH. ZordanV. YangY. AndrewsS.: Adaptive Distributed Simulation of Fluids and Rigid Bodies. InProceedings of the 17th ACM SIGGRAPH Conference on Motion Interaction and Games(Nov.2024). doi:10.1145\/3677388.3696334. 2","DOI":"10.1145\/3677388.3696334"},{"key":"e_1_2_7_48_2","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417798"},{"key":"e_1_2_7_49_2","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555474"},{"key":"e_1_2_7_50_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12578"},{"key":"e_1_2_7_51_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2021.114292"},{"key":"e_1_2_7_52_2","doi-asserted-by":"publisher","DOI":"10.1145\/3606933"},{"key":"e_1_2_7_53_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13349"},{"key":"e_1_2_7_54_2","doi-asserted-by":"publisher","DOI":"10.1002\/cav.70057"},{"key":"e_1_2_7_55_2","doi-asserted-by":"publisher","DOI":"10.1145\/3592115"},{"key":"e_1_2_7_56_2","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555476"},{"key":"e_1_2_7_57_2","doi-asserted-by":"crossref","unstructured":"ZarifiO. BattyC.: A positive\u2010definite cut\u2010cell method for strong two\u2010way coupling between fluids and deformable bodies. InProceedings of the ACM SIGGRAPH \/ Eurographics Symposium on Computer Animation(2017). doi:10.1145\/3099564.3099572. 2","DOI":"10.1145\/3099564.3099572"},{"key":"e_1_2_7_58_2","doi-asserted-by":"publisher","DOI":"10.3390\/computers9020023"}],"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.70559","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/cgf.70559","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.70559","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T11:19:15Z","timestamp":1786533555000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/cgf.70559"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,12]]},"references-count":58,"alternative-id":["10.1111\/cgf.70559"],"URL":"https:\/\/doi.org\/10.1111\/cgf.70559","archive":["Portico"],"relation":{},"ISSN":["0167-7055","1467-8659"],"issn-type":[{"value":"0167-7055","type":"print"},{"value":"1467-8659","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,12]]},"assertion":[{"value":"2026-08-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70559"}}