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Graph."],"published-print":{"date-parts":[[2019,8,31]]},"abstract":"<jats:p>\n            In this paper, we introduce BiMocq\n            <jats:sup>2<\/jats:sup>\n            , an unconditionally stable, pure Eulerianbased advection scheme to efficiently preserve the advection accuracy of all physical quantities for long-term fluid simulations. Our approach is built upon the method of characteristic mapping (MCM). Instead of the costly evaluation of the temporal characteristic integral, we evolve the mapping function itself by solving an advection equation for the mappings. Dual mesh characteristics (DMC) method is adopted to more accurately update the mapping. Furthermore, to avoid visual artifacts like instant blur and temporal inconsistency introduced by re-initialization, we introduce multi-level mapping and back and forth error compensation. We conduct comprehensive 2D and 3D benchmark experiments to compare against alternative advection schemes. In particular, for the vortical flow and level set experiments, our method outperforms almost all state-of-art hybrid schemes, including FLIP, PolyPic and Particle-Level-Set, at the cost of only two Semi-Lagrangian advections. Additionally, our method does not rely on the particle-grid transfer operations, leading to a highly parallelizable pipeline. As a result, more than 45\u00d7 performance acceleration can be achieved via even a straightforward porting of the code from CPU to GPU.\n          <\/jats:p>","DOI":"10.1145\/3306346.3322945","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T19:04:08Z","timestamp":1562958248000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":59,"title":["Efficient and conservative fluids using bidirectional mapping"],"prefix":"10.1145","volume":"38","author":[{"given":"Ziyin","family":"Qu","sequence":"first","affiliation":[{"name":"AICFVE and University of Pennsylvania"}]},{"given":"Xinxin","family":"Zhang","sequence":"additional","affiliation":[{"name":"AICFVE"}]},{"given":"Ming","family":"Gao","sequence":"additional","affiliation":[{"name":"University of Pennsylvania"}]},{"given":"Chenfanfu","family":"Jiang","sequence":"additional","affiliation":[{"name":"University of Pennsylvania"}]},{"given":"Baoquan","family":"Chen","sequence":"additional","affiliation":[{"name":"Peking University"}]}],"member":"320","published-online":{"date-parts":[[2019,7,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073625"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766935"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073606"},{"key":"e_1_2_2_4_1","volume-title":"Fluid Simulation for Computer Graphics","author":"Bridson R.","unstructured":"R. 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Vortex methods: theory and practice. Cambridge university press.  Georges-Henri Cottet Petros D Koumoutsakos D Petros et al. 2000. Vortex methods: theory and practice. Cambridge university press."},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.5555\/949845.949893"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1189762.1189766"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7166"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566645"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/2487228.2487230"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383260"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882336"},{"key":"e_1_2_2_15_1","volume-title":"Computer Graphics Forum","author":"Ferstl Florian","unstructured":"Florian Ferstl , Ryoichi Ando , Chris Wojtan , R\u00fcdiger Westermann , and Nils Thuerey . 2016. Narrow band FLIP for liquid simulations . In Computer Graphics Forum , Vol. 35 . Wiley Online Library , 225--232. Florian Ferstl, Ryoichi Ando, Chris Wojtan, R\u00fcdiger Westermann, and Nils Thuerey. 2016. Narrow band FLIP for liquid simulations. In Computer Graphics Forum, Vol. 35. Wiley Online Library, 225--232."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383261"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/3130800.3130878"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/3130800.3130879"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/3272127.3275044"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766996"},{"key":"e_1_2_2_22_1","volume-title":"FlowFixer: Using BFECC for Fluid Simulation. In Eurographics Conference on Natural Phenomena. 51--56","author":"Kim B.","unstructured":"B. Kim , Y. Liu , I. Llamas , and J. Rossignac . 2005 . FlowFixer: Using BFECC for Fluid Simulation. In Eurographics Conference on Natural Phenomena. 51--56 . B. Kim, Y. Liu, I. Llamas, and J. Rossignac. 2005. FlowFixer: Using BFECC for Fluid Simulation. In Eurographics Conference on Natural Phenomena. 51--56."},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1399504.1360649"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1964921.1964931"},{"key":"e_1_2_2_25_1","doi-asserted-by":"crossref","unstructured":"T. T. Lim and T. B. Nickels. 1992. Instability and reconnection in the head-on collision of two vortex rings. Nature 357 (05 1992) 225--227.  T. T. Lim and T. B. Nickels. 1992. Instability and reconnection in the head-on collision of two vortex rings. 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