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The reality and real-time performance have always been the research hot-point of fluid simulation. Aiming at the unstable fluid surface motion in the scenes with complex terrain, in this paper, we propose an adaptive fluid velocity control force calculation model based on terrain difference, and a stable SPH numerical model for solving the shallow water equations is established. In this proposed numerical model, firstly we reduce the simulation domain from three-dimensional space to two-dimensional surface for reducing calculation quantity, and the water depth is represented by the density of particles at the meantime. Secondly, to ensure that the number of neighborhood particles is stable within a fixed range and to improve the accuracy of simulation, we apply a variable smoothing length to our numerical model. Then, an adaptive fluid velocity control force calculation model is introduced based on terrain difference, in which the velocity and position of particles are corrected by calculating the terrain difference caused by particle movement between each time step. The coordinates on terrain used for the calculation of terrain difference are dynamically chosen by the density of the particles. To improve the real-time performance of simulation, a screen space fluid rendering method is used to refrain the extraction and reconstruction of fluid surface. The numerical calculation and fluid surface rendering both load on the GPU for parallel execution. The simulation result shows that the proposed method can effectively improve the unstable fluid surface movement in scenes with complex terrain while reaching a real-time interaction level. The density and pressure are evenly distributed during the simulation.
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Keywords:
- smoothed particle hydrodynamics /
- shallow water equations /
- parallel computing /
- complex terrain
[1] Harada T, Koshizuka S, Kawaguchi Y 2007 Proceedings of the 23rd Spring Conference on Computer Graphics Budmerice, Slovakia, April 26−28, 2007 p191
[2] Mastin G A, Watterberg P A, Mareda J F 1987 IEEE Comput. Graph. 7 16Google Scholar
[3] Chentanez N, Müller M, Kim T Y 2015 IEEE T Vis. Comput. Gr. 21 1116Google Scholar
[4] Monaghan J J 1994 J. Comput. Phys. 110 399Google Scholar
[5] Brodtkorb A R, Sætra M L, Altinakar M 2012 Comput. Fluids 55 1Google Scholar
[6] Monaghan J J 1992 Annu. Rev. Astron. Astr. 30 543Google Scholar
[7] Swegle J W, Hicks D L, Attaway S W 1995 J. Comput. Phys. 116 123Google Scholar
[8] Ata R, Soulaïmani A 2005 Int. J. Numer. Meth. Fl. 47 139Google Scholar
[9] Rodriguez-Paz M, Bonet J 2005 Comput. Struct. 83 1396Google Scholar
[10] Chang T J, Kao H M, Chang K H, Hsu M H 2011 J. Hydrol. 408 78Google Scholar
[11] Xia X L, Liang Q H, Pastor M, Zou W L, Zhuang Y F 2013 Adv. Water Resour. 59 25Google Scholar
[12] Chentanez N, Müller M 2010 Symposium on Computer Animation Goslar, Germany, July 2−4, 2010 p197
[13] De Leffe M, Le Touzé D, Alessandrini B 2010 J. Hydraul. Res. 48 118Google Scholar
[14] Chládek M, Ďurikovič R 2015 Comput. Graph. 53 170Google Scholar
[15] Solenthaler B, Bucher P, Chentanez N, Müller M 2011 VRIPHYS 11: 8th Workshop on Virtual Reality Interactions and Physical Simulations Lyon, France, December 5−6, 2011 p39
[16] Lee H, Han S 2010 Visual Comput. 26 865Google Scholar
[17] 张海超, 郑丹晨, 边茂松, 韩敏 2016 物理学报 65 244701Google Scholar
Zhang H C, Zheng D C, Bian M S, Han M 2016 Acta Phys. Sin. 65 244701Google Scholar
[18] Capecelatro J 2018 J. Comput. Phys. 356 174Google Scholar
[19] van der Laan W J, Green S, Sainz M 2009 Proceedings of the 2009 Symposium on Interactive 3D Graphics and Games Boston, Massachusetts, February 27−March 1, 2009 p91
[20] Müller M, Solenthaler B, Keiser R, Gross M 2005 Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation Los Angeles, California, July 29−31, 2005 p237
[21] Fujisawa M, Nakada T, Mikawa M 2017 J. Inform. Processing. 25 486Google Scholar
[22] Müller M, Charypar D, Gross M H 2003 Symposium on Computer Animation Goslar, Germany, July 26−27, 2003 p154
[23] Liu M B, Liu G R, Lam K Y 2002 Shock Waves 12 181Google Scholar
[24] Akinci N, Ihmsen M, Akinci G, Solenthaler B, Teschner M 2012 ACM T. Graphic. 31 1
[25] Müller M, Schirm S, Duthaler S 2007 Proceedings of the 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation Goslar, Germany, August 2, 2007 p9
[26] dos Santos Brito C J, Almeida M W S, Vieira-e-Silva A L B, Teixeira J M X N, Teichrieb V 2017 2017 19th Symposium on Virtual and Augmented Reality (SVR). IEEE Curitiba, Brazil, November 1−4, 2017 p309
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图 12 爱荷华场景水淹情况示意图 (a) 依据历年水淹范围统计的淹没概率图; (b) 2008年6月爱荷华雨洪淹没范围图; (c) 水深25 ft, 流量31200 cfs情况下淹没范围图; (d) 本文淹没模拟结果示意图
Figure 12. The flood inundation maps of iowa scene: (a) The inundation probability map based on the statistics of the flooding range over the years; (b) the flood inundation map of iowa in June, 2008; (c) map of inundation range under the condition of 25 ft water depth and 31200 cfs water flow; (d) the simulated inundation map of our method.
表 1 实验参数取值
Table 1. The values of parameters in experiment.
物理量 值 单位 粒子半径 $ r $ 0.5 m 时间步长 $ \Delta t $ 0.02 s 初始粒子间距 $ {r_0} $ 1 m 初始搜索半径 $ {h_0} $ 2.66 m 静密度 $ {\rho _0} $ 1000 kg/${{\rm{m}}^3}$ 粒子质量 $ m $ 1000 kg 气体常数 $ k $ 10 — 黏度系数 $ \mu $ 0.1 — 表 2 实际水深与模拟水深数据对比
Table 2. Comparison between actual and simulated water depth
点位 模拟水深/m 实测水深/m 相对误差/% A 1.29 1.43 9.79 B 1.51 1.65 8.48 C 1.97 1.92 2.60 D 1.50 1.40 7.14 -
[1] Harada T, Koshizuka S, Kawaguchi Y 2007 Proceedings of the 23rd Spring Conference on Computer Graphics Budmerice, Slovakia, April 26−28, 2007 p191
[2] Mastin G A, Watterberg P A, Mareda J F 1987 IEEE Comput. Graph. 7 16Google Scholar
[3] Chentanez N, Müller M, Kim T Y 2015 IEEE T Vis. Comput. Gr. 21 1116Google Scholar
[4] Monaghan J J 1994 J. Comput. Phys. 110 399Google Scholar
[5] Brodtkorb A R, Sætra M L, Altinakar M 2012 Comput. Fluids 55 1Google Scholar
[6] Monaghan J J 1992 Annu. Rev. Astron. Astr. 30 543Google Scholar
[7] Swegle J W, Hicks D L, Attaway S W 1995 J. Comput. Phys. 116 123Google Scholar
[8] Ata R, Soulaïmani A 2005 Int. J. Numer. Meth. Fl. 47 139Google Scholar
[9] Rodriguez-Paz M, Bonet J 2005 Comput. Struct. 83 1396Google Scholar
[10] Chang T J, Kao H M, Chang K H, Hsu M H 2011 J. Hydrol. 408 78Google Scholar
[11] Xia X L, Liang Q H, Pastor M, Zou W L, Zhuang Y F 2013 Adv. Water Resour. 59 25Google Scholar
[12] Chentanez N, Müller M 2010 Symposium on Computer Animation Goslar, Germany, July 2−4, 2010 p197
[13] De Leffe M, Le Touzé D, Alessandrini B 2010 J. Hydraul. Res. 48 118Google Scholar
[14] Chládek M, Ďurikovič R 2015 Comput. Graph. 53 170Google Scholar
[15] Solenthaler B, Bucher P, Chentanez N, Müller M 2011 VRIPHYS 11: 8th Workshop on Virtual Reality Interactions and Physical Simulations Lyon, France, December 5−6, 2011 p39
[16] Lee H, Han S 2010 Visual Comput. 26 865Google Scholar
[17] 张海超, 郑丹晨, 边茂松, 韩敏 2016 物理学报 65 244701Google Scholar
Zhang H C, Zheng D C, Bian M S, Han M 2016 Acta Phys. Sin. 65 244701Google Scholar
[18] Capecelatro J 2018 J. Comput. Phys. 356 174Google Scholar
[19] van der Laan W J, Green S, Sainz M 2009 Proceedings of the 2009 Symposium on Interactive 3D Graphics and Games Boston, Massachusetts, February 27−March 1, 2009 p91
[20] Müller M, Solenthaler B, Keiser R, Gross M 2005 Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation Los Angeles, California, July 29−31, 2005 p237
[21] Fujisawa M, Nakada T, Mikawa M 2017 J. Inform. Processing. 25 486Google Scholar
[22] Müller M, Charypar D, Gross M H 2003 Symposium on Computer Animation Goslar, Germany, July 26−27, 2003 p154
[23] Liu M B, Liu G R, Lam K Y 2002 Shock Waves 12 181Google Scholar
[24] Akinci N, Ihmsen M, Akinci G, Solenthaler B, Teschner M 2012 ACM T. Graphic. 31 1
[25] Müller M, Schirm S, Duthaler S 2007 Proceedings of the 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation Goslar, Germany, August 2, 2007 p9
[26] dos Santos Brito C J, Almeida M W S, Vieira-e-Silva A L B, Teixeira J M X N, Teichrieb V 2017 2017 19th Symposium on Virtual and Augmented Reality (SVR). IEEE Curitiba, Brazil, November 1−4, 2017 p309
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