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Smoothed particle hydrodynamics (SPH) method is a kind of meshless method, which is used to solve the problem of fluid simulation without complex operations of the grids. To reduce the computational complexity, SPH method based on the two-dimensional shallow water equations is employed to establish a fluid model. In large scale scenes, taking into account the high computational complexity and the serious distortion problems, in this paper we introduce an improved two-dimensional SPH algorithm according to the shallow water equations. The proposed method with two-dimensional complexity is obtained by discretizing the two-dimensional shallow water equations with SPH, and the depth of water is introduced as the particle's property. The problem of increased amount of calculation cannot be well solved by using traditional neighboring particle search method based on tree structure. To improve the efficiency of search and simplify the search operation of neighborhood particles, in this paper we introduce a point-in-box search algorithm and put forward a neighboring particles searching method on the basis of dynamic grid. Besides, for large scale scenes, by considering that the virtual particle method provides slow computation speed with complex boundary condition, the type-one virtual particles are utilized to ensure that the borders can be calculated precisely by combining the punish force to prevent the phenomenon of particle boundary penetrating. Therefore, a method is further obtained to handle boundary condition efficiently by combining the virtual particles with punish force in this paper. In the process of rendering, the fluid surface is first determined by mapping and interpolating particles into regular grids without the complex reconstruction of surface in three-dimensional. Then, we utilize the bilinear interpolation method to deal with the problem of missing values, and the surface grids are further densified. With OpenSceneGraph three-dimensional render engine, OpenGL Shading Language is adopted to speed up the rendering speed, and in this way, the real-time fluid simulation of large scale scenes can be further achieved. With the basic KD tree searching method employed in the simulations, the comparative experiments are provided to verify effectiveness of the proposed searching method based on dynamic grid. Given the data set obtained from random points, experimental results demonstrate that the method in this paper can be used to solve the problem of neighboring particles searching in large scale scenes. To show the effectiveness of the proposed method on the basis of the virtual particles and the punish force, another experiment based on the collapsing of a water column is further provided. Besides, in this paper we conduct an experiment on a certain actual reservoir terrain to prove that the proposed method can be applied to fluid simulation of large scale scenes.
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Keywords:
- smoothed particle hydrodynamics /
- shallow water equations /
- fluid simulation /
- three-dimensional simulation
[1] Lucy L B 1977 Astron. J. 82 1013
[2] Prakash M, Rothauge K, Cleary P W 2014 Appl. Math. Model. 38 1534
[3] Kipfer P, Westermann R 2006 Proceedings of Graphics Interface 2006 Quebec City, Canada, June 7-9, 2006 p41
[4] Ata R, Soulaïmani A 2005 Int. J. Numer. Meth. Fl. 47 139
[5] de Leffe M, Le Touzé D, Alessandrini B 2010 J. Hydraul. Res. 48 118
[6] Lee H, Han S 2010 Visual Comput. 26 865
[7] Solenthaler B, Bucher P, Chentanez N, Mller M, Gross M 2011 Proceedings of Workshop in Virtual Reality Interactions and Physical Simulations Lyon, France, December 5-6, 2011 p39
[8] He X W, Liu N, Wang G P, Zhang F J, Li S, Shao S D, Wang H A 2012 ACM T. Graphic. 31 439
[9] Cornelis J, Ihmsen M, Teschner M 2015 Comput. Graph-UK 52 72
[10] He J, Chen X, Wang Z Y, Cao C, Yan H, Peng Q S 2010 Visual Comput. 26 243
[11] Liu H, Qiang H F, Chen F Z, Han Y W, Fan S J 2015 Acta Phys. Sin. 64 094701 (in Chinese)[刘虎, 强洪夫, 陈福振, 韩亚伟, 范树佳2015物理学报 64 094701]
[12] Han Y W, Qiang H F, Zhao J L, Gao W R 2013 Acta Phys. Sin. 62 044702 (in Chinese)[韩亚伟, 强洪夫, 赵玖玲, 高巍然2013物理学报 62 044702]
[13] Hu D A, Long T, Xiao Y H, Han X, Gu Y T 2014 Comput. Method. Appl. M. 276 266
[14] Xia X L, Liang Q H 2015 Environ. Modell Softw. 75 28
[15] Goswami P, Schlegel P, Solenthaler B, Pajarola R 2010 Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation Madrid, Spain, July 2-4, 2010 p55
[16] Yang L P, Li S, Hao A, Qin H 2012 Comput. Graph. Forum. 31 2037
[17] Rodriguez-Paz M, Bonet J 2005 Comput. Struct. 83 1396
[18] Liu M B, Liu G R, Lam K Y 2003 Comput. Appl. Math. 155 263
[19] Ihmsen M, Orthmann J, Solenthaler B, Kolb A, Teschner M 2014 Proceedings of Eurographics 2014 State of the Art Reports Strasbourg, April 7-11, 2014 p21
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[1] Lucy L B 1977 Astron. J. 82 1013
[2] Prakash M, Rothauge K, Cleary P W 2014 Appl. Math. Model. 38 1534
[3] Kipfer P, Westermann R 2006 Proceedings of Graphics Interface 2006 Quebec City, Canada, June 7-9, 2006 p41
[4] Ata R, Soulaïmani A 2005 Int. J. Numer. Meth. Fl. 47 139
[5] de Leffe M, Le Touzé D, Alessandrini B 2010 J. Hydraul. Res. 48 118
[6] Lee H, Han S 2010 Visual Comput. 26 865
[7] Solenthaler B, Bucher P, Chentanez N, Mller M, Gross M 2011 Proceedings of Workshop in Virtual Reality Interactions and Physical Simulations Lyon, France, December 5-6, 2011 p39
[8] He X W, Liu N, Wang G P, Zhang F J, Li S, Shao S D, Wang H A 2012 ACM T. Graphic. 31 439
[9] Cornelis J, Ihmsen M, Teschner M 2015 Comput. Graph-UK 52 72
[10] He J, Chen X, Wang Z Y, Cao C, Yan H, Peng Q S 2010 Visual Comput. 26 243
[11] Liu H, Qiang H F, Chen F Z, Han Y W, Fan S J 2015 Acta Phys. Sin. 64 094701 (in Chinese)[刘虎, 强洪夫, 陈福振, 韩亚伟, 范树佳2015物理学报 64 094701]
[12] Han Y W, Qiang H F, Zhao J L, Gao W R 2013 Acta Phys. Sin. 62 044702 (in Chinese)[韩亚伟, 强洪夫, 赵玖玲, 高巍然2013物理学报 62 044702]
[13] Hu D A, Long T, Xiao Y H, Han X, Gu Y T 2014 Comput. Method. Appl. M. 276 266
[14] Xia X L, Liang Q H 2015 Environ. Modell Softw. 75 28
[15] Goswami P, Schlegel P, Solenthaler B, Pajarola R 2010 Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation Madrid, Spain, July 2-4, 2010 p55
[16] Yang L P, Li S, Hao A, Qin H 2012 Comput. Graph. Forum. 31 2037
[17] Rodriguez-Paz M, Bonet J 2005 Comput. Struct. 83 1396
[18] Liu M B, Liu G R, Lam K Y 2003 Comput. Appl. Math. 155 263
[19] Ihmsen M, Orthmann J, Solenthaler B, Kolb A, Teschner M 2014 Proceedings of Eurographics 2014 State of the Art Reports Strasbourg, April 7-11, 2014 p21
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