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Differing from existing implicit formulations, our approach reconstructs the velocity field from a target velocity gradient. This gradient encodes a desired shear-rate damping and preserves the velocity divergence that is introduced by the SPH pressure solver to counteract density deviations. The target gradient ensures that pressure and viscosity computation do not interfere. Therefore, only one pressure projection step is required, which is in contrast to state-of-the-art implicit Eulerian formulations. While our model differs from true viscosity in that vorticity diffusion is not encoded in the target gradient, it nevertheless captures many of the qualitative behaviors of viscous liquids. Our formulation can easily be incorporated into complex scenarios with one- and two-way coupled solids and multiple fluid phases with different densities and viscosities.<\/jats:p>","DOI":"10.1145\/2766925","type":"journal-article","created":{"date-parts":[[2015,7,28]],"date-time":"2015-07-28T12:26:38Z","timestamp":1438086398000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":74,"title":["An implicit viscosity formulation for SPH fluids"],"prefix":"10.1145","volume":"34","author":[{"given":"Andreas","family":"Peer","sequence":"first","affiliation":[{"name":"University of Freiburg"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Markus","family":"Ihmsen","sequence":"additional","affiliation":[{"name":"University of Freiburg"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jens","family":"Cornelis","sequence":"additional","affiliation":[{"name":"University of Freiburg"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthias","family":"Teschner","sequence":"additional","affiliation":[{"name":"University of Freiburg"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2015,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.02096.x"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185558"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508395"},{"key":"e_1_2_2_4_1","volume-title":"Proceedings of the 2008 ACM SIGGRAPH\/Eurographics symposium on computer animation, Eurographics Association, 219--228","author":"Batty C."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2019406.2019421"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185609"},{"key":"e_1_2_2_7_1","volume-title":"Proceedings of the 2007 ACM SIGGRAPH\/Eurographics symposium on Computer animation, Eurographics Association, 209--217","author":"Becker M."},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.5555\/2381692.2381696"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2014.07.004"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12346"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778853"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/545261.545289"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1643928.1643954"},{"key":"e_1_2_2_14_1","volume-title":"VR Innovation (ISVRI), 2011 IEEE International Symposium on, IEEE, 199--205","author":"Chang Y."},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073368.1073400"},{"key":"e_1_2_2_16_1","volume-title":"Proceedings of the Computer Graphics International","author":"Dagenais F.","year":"2012"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/SIBGRAPI.2014.47"},{"key":"e_1_2_2_18_1","volume-title":"Proceedings of the Eurographics Workshop on Computer Animation and Simulation '96","author":"Desbrun M."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/965400.965559"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1006\/gmip.1996.0039"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1599470.1599488"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015746"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073283"},{"key":"e_1_2_2_24_1","volume-title":"Proceedings VRIPHYS, VRIPHYS, 79--88","author":"Ihmsen M."},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01832.x"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2013.105"},{"key":"e_1_2_2_27_1","unstructured":"Ihmsen M. 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