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Many previous SPH porous flow methods reduce particle volumes as they transition across the solid-fluid interface, resulting in significant stability issues. We instead allow fluid and solid to overlap by deriving a new density estimation. This further allows us to extend SPH pressure solvers to take local porosity into account and results in strict enforcement of incompressibility. As a result, we can simulate porous flow using physically consistent pressure forces between fluid and solid. In contrast to previous SPH porous flow methods, which use explicit forces for internal fluid flow, we employ implicit non-pressure forces. These we solve as a linear system and strongly couple with fluid viscosity and solid elasticity. We capture the most common effects observed in porous flow, namely drag, buoyancy and capillary action due to adhesion. To achieve elastic behavior change based on local fluid saturation, such as bloating or softening, we propose an extension to the elasticity model. We demonstrate the efficacy of our model with various simulations that showcase the different aspects of porous flow behavior. To summarize, our system of strongly coupled non-pressure forces and enforced incompressibility across overlapping phases allows us to naturally model and stably simulate complex porous interactions.<\/jats:p>","DOI":"10.1145\/3763325","type":"journal-article","created":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T17:15:39Z","timestamp":1764868539000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Implicit Incompressible Porous Flow using SPH"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-1024-6549","authenticated-orcid":false,"given":"Timna","family":"B\u00f6ttcher","sequence":"first","affiliation":[{"name":"Visual Computing Institute, RWTH Aachen University, Aachen, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4427-2377","authenticated-orcid":false,"given":"Lukas","family":"Westhofen","sequence":"additional","affiliation":[{"name":"Visual Computing Institute, RWTH Aachen University, Aachen, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3920-7765","authenticated-orcid":false,"given":"Stefan Rhys","family":"Jeske","sequence":"additional","affiliation":[{"name":"Visual Computing Institute, RWTH Aachen University, Aachen, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1908-4027","authenticated-orcid":false,"given":"Jan","family":"Bender","sequence":"additional","affiliation":[{"name":"Visual Computing Institute, RWTH Aachen University, Aachen, Germany"}]}],"member":"320","published-online":{"date-parts":[[2025,12,4]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508395"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185558"},{"key":"e_1_2_2_3_1","unstructured":"Jan Bender et al. 2025. 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