脉动风场中烟雾模拟方法的优化研究
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摘要
在计算机图形学中,真实的再现烟雾等自然现象一直是最具有挑战性研究方向之一。传统的粒子系统和纹理映射等方法模拟出烟雾真实感较差,无法满足高真实性要求。随着流体力学领域中对流体物理特性的研究日益成熟,基于物理的方法得到了广泛的应用,它从烟雾的内在物理特性出发,建立精确的物理模型,模拟出高精确度的烟雾动画。本文采用基于物理的方法进行烟雾模拟,并针对烟雾模拟的实时性和真实性要求进行研究。
首先,在提高实时性方面,采用非粘性不可压缩Navier-Stokes方程组建立烟雾物理模型,利用有限差分法结合GPU加速技术求解烟雾物理方程,将求解区域离散化,并对烟雾基本物理方程进行简化,减少计算量。同时,应用MacCormack方法求解对流项,减少传统方法的求解步骤,提高计算速度并保证求解过程的无条件稳定性。
其次,在提高真实性方面,引入风场的作用,使烟雾的形态和运动更加逼真自然。采用优化的卡门谱建立风场的互谱密度矩阵,引入特征正交分解(POD)技术求解矩阵,并利用快速傅立叶变换(FFT)技术求出脉动风在频域空间的速度场,将脉动风场以外力的形式加入到描述烟雾运动的物理方程中,实现风场与烟雾的交互作用。
再次,将烟雾的重力、热浮力和漩涡约束力加入到影响烟雾运动的特征因素集中,改善烟雾的运动细节,增强运动的真实性。此外,考虑烟雾的密度和温度随速度场的变化,以准确的计算烟雾的重力和热浮力。
最后,利用VC++语言和开放性图形接口OpenGL设计烟雾的实时仿真系统,对改进后的烟雾模拟算法进行验证,实验证明:利用本文的算法可以实时的生成在脉动风环境下逼真自然的烟雾。
The simulation of natural phenomena such as smoke, has been one of the most challenging research areas in computer graphics. The smoke image generated by traditional particle system and the texture mapping is poor and can hardly meet the requirements of high authenticity. As extensive research in fluid dynamics has been done, physically based method has been widely used to simulate smoke. It analyses the inherent physical characteristics of the smoke, and establishes an accurate physical model to obtain the realistic smoke. We adopt the physical method to simulate the smoke, and focus on our researches on the real-time and the reality of the simulation.
Firstly, in order to improve the real-time quality, we use non-viscous incompressible Navier-Stokes equations to establish the physical model of the smoke, solve physical equations by the finite difference method and GPU acceleration, discrete the computational domain, and simplify the basic physics equations to reduce the computational time. In addition, we adopt MacCormack method to solve the advection item of the Navier-Stokes equation, so as to reduce the solving steps of traditional methods, improve the computational speed and ensure the solving processes are unconditional stable.
Secondly, for the purpose of improving the authentic performance, we introduce the role of wind field, so that the shape and movement of the smoke will be more realistic and natural. We use optimized Karman spectrum to establish cross-spectral density matrix of the wind field, then introduce Proper Orthogonal Decomposition(POD) technique for solving the matrix, and then calculate the fluctuating wind velocity in the frequency domain space by the Fast Fourier Transform(FFT). Finally, the wind fields are considered as the outside forces to be added into the physical equations of the smoke, so the interaction of the fluctuating wind and the smoke is realized.
Thirdly, the gravity, thermal buoyancy and vorticity confinement force, which greatly affect the smoke’s movement, are added into the smoke field, to improve the details and the reality of the smoke’s movement. Moreover, we also consider that the smoke’s density and temperature changes with the velocity field, to ensure the smoke’s gravity and buoyancy are calculated accurately.
Finally, in order to verify our improved smoke simulation algorithms, we use the VC++ language and Open Graphics Library to design the real-time smoke simulation system. Experiment results show: our algorithms can run in real-time and the smoke effects are of great reality and nature in the turbulent wind environment.
首先,在提高实时性方面,采用非粘性不可压缩Navier-Stokes方程组建立烟雾物理模型,利用有限差分法结合GPU加速技术求解烟雾物理方程,将求解区域离散化,并对烟雾基本物理方程进行简化,减少计算量。同时,应用MacCormack方法求解对流项,减少传统方法的求解步骤,提高计算速度并保证求解过程的无条件稳定性。
其次,在提高真实性方面,引入风场的作用,使烟雾的形态和运动更加逼真自然。采用优化的卡门谱建立风场的互谱密度矩阵,引入特征正交分解(POD)技术求解矩阵,并利用快速傅立叶变换(FFT)技术求出脉动风在频域空间的速度场,将脉动风场以外力的形式加入到描述烟雾运动的物理方程中,实现风场与烟雾的交互作用。
再次,将烟雾的重力、热浮力和漩涡约束力加入到影响烟雾运动的特征因素集中,改善烟雾的运动细节,增强运动的真实性。此外,考虑烟雾的密度和温度随速度场的变化,以准确的计算烟雾的重力和热浮力。
最后,利用VC++语言和开放性图形接口OpenGL设计烟雾的实时仿真系统,对改进后的烟雾模拟算法进行验证,实验证明:利用本文的算法可以实时的生成在脉动风环境下逼真自然的烟雾。
The simulation of natural phenomena such as smoke, has been one of the most challenging research areas in computer graphics. The smoke image generated by traditional particle system and the texture mapping is poor and can hardly meet the requirements of high authenticity. As extensive research in fluid dynamics has been done, physically based method has been widely used to simulate smoke. It analyses the inherent physical characteristics of the smoke, and establishes an accurate physical model to obtain the realistic smoke. We adopt the physical method to simulate the smoke, and focus on our researches on the real-time and the reality of the simulation.
Firstly, in order to improve the real-time quality, we use non-viscous incompressible Navier-Stokes equations to establish the physical model of the smoke, solve physical equations by the finite difference method and GPU acceleration, discrete the computational domain, and simplify the basic physics equations to reduce the computational time. In addition, we adopt MacCormack method to solve the advection item of the Navier-Stokes equation, so as to reduce the solving steps of traditional methods, improve the computational speed and ensure the solving processes are unconditional stable.
Secondly, for the purpose of improving the authentic performance, we introduce the role of wind field, so that the shape and movement of the smoke will be more realistic and natural. We use optimized Karman spectrum to establish cross-spectral density matrix of the wind field, then introduce Proper Orthogonal Decomposition(POD) technique for solving the matrix, and then calculate the fluctuating wind velocity in the frequency domain space by the Fast Fourier Transform(FFT). Finally, the wind fields are considered as the outside forces to be added into the physical equations of the smoke, so the interaction of the fluctuating wind and the smoke is realized.
Thirdly, the gravity, thermal buoyancy and vorticity confinement force, which greatly affect the smoke’s movement, are added into the smoke field, to improve the details and the reality of the smoke’s movement. Moreover, we also consider that the smoke’s density and temperature changes with the velocity field, to ensure the smoke’s gravity and buoyancy are calculated accurately.
Finally, in order to verify our improved smoke simulation algorithms, we use the VC++ language and Open Graphics Library to design the real-time smoke simulation system. Experiment results show: our algorithms can run in real-time and the smoke effects are of great reality and nature in the turbulent wind environment.
引文
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23 Dupont T.F, Liu Y. Back and forth error compensation and correction methods for semi-Lagrangian schemes with application to level set interface computations. Mathematics of Computation, 2007, 76(258):647-668
24 Crane K., LLAMAS I, TARIQ S. Real-time simulation and rendering of 3d fluids. Urbana-Champaign: University of Illinois, 2007
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26 H. Schechter, R. Bridson. Evolving Sub-Grid Turbulence for Smoke Animation. ACM SIGGRAPH Symposium On Computer Animation, 2008
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32湛永松,石民勇,费广正.基于流体力学方程的二维烟雾模拟.中国传媒大学学报, 2007, 14(1):68-72
33湛永松,杨明浩,石民勇,等.保持自然特征的烟雾快速生成系统.系统仿真学报, 2007, 19(19):4460-4463
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39 Frank Losasso, Frederic Gibou, Ronald Fedkiw. Simulation Water and Smoke with an Octree Data Structure. ACM SIGGRAPH, 2004, 23(3):457-462.
40 Bryan Feldman, James O'Brien, Bryan Klingner. Animating Gases with Hybrid Meshes. ACM Transactions on Graphics, 2005, 24(3):904-909.
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44 Jang Yoojin, lhm.Insung. Chemical Kinetics-assisted, Path-based Smoke Simulation. Computer Animation and Virtual Worlds, 2009, 20(2-3):247-256
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62 A. Treuille, A. McNamara, Z. Popovic, J. Stam. Keyframe Control of Smoke Simulations. ACM Transactions on Graphics(TOG),2003,22(3):716-723
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2 C.W. Reynolds. Flocks, Herds, and Schools: A Distributed Behavioral Model. Association of Computing Machinery, ACM, 1987,21:25-34
3 K. Sims. Particle Animation and Rendering Using Data Parallel Computation. Computer Graphics,1990,24(4):405-413
4 R. Szeliski, D. Tonnesen. Surface Modeling with Oriented Particle Systems. Computer Graphics,1992,26(3):185-194
5 M. Sabo. Improving Advanced Particle System by Adding Property Milestones to Particle Life Cycle. CESCG’04 proceedings,Maribor,Slovenia,2004:96-99
6 T. Iimonen. The Second Order Particle System. WSCG,2003,11(1):1213-6972
7童若锋,陈凌钧,汪国昭,等.烟雾的快速模拟.软件学报, 1999,10(6):647-651
8鄢来斌,李思昆,等.动态浓烟建模与实时绘制技术研究.计算机工程与科学, 2001,23(11):68-74
9 A. Selle, N. Rasmussen, R. Fedkiw. A Vortex Particle Method for Smoke, Water and Explosions.ACM Transactions on Graphics, 2005,24(3):910-914
10 Morgan McGuire, Andi Fein. Real-time rendering of cartoon smoke and clouds. Annecy Animation festival. Non-Photorealistic Animation and Rendering, Annecy, France, ACM, New York, NY, USA,2006:21-26
11李维松,周晓光,王润杰,等.基于粒子系统的烟雾模拟.计算机仿真, 2007, 24(9):199-201
12袁雪霞,尹新富.烟雾的快速模拟.计算机工程与设计, 2008, 29(9):2392-2394
13王盛邦,纪庆革.基于粒子系统的实时烟雾仿真.中山大学学报, 2008, 47(2):9-13
14 NengWen Zhou, Yunbo Rao. Real Time Dense Smoke Simulation Based Particle System. Proceedings-2nd 2008 International Symposium on Intelligent Information Technology Application Workshop, 2008:809-813
15陈志宏,张正兰.动画烟雾动态模拟算法研究.计算机仿真, 2009, 26(2):217-220
16唐勇,李晓艳,吕梦雅,等.基于粒子生成函数的烟雾模拟.计算机应用研究, 2010, 27(2):754-756
17 J. Kajiya. Ray Tracing Volume Densities//Proceedings of SIGGRAPH, Minneapolis, Minnesota, USA, 1984:165-174
18 N. Foster, D. Metaxas. Modeling the Motion of a Hot, Turbulent Gas. In Proceedings of SIGGRAPH’97,1997,181-188
19 J. Stam. Stable Fluids//Proceedings of SIGGRAPH, Los Angeles, California, USA, 1999:121-128
20 R. Fedkiw, J. Stam, H. Jensen. Visual Simulation of Smoke//Proceedings of SIGGRAPH, Los Angeles, California, USA, 2001:15-22
21 N. Rasmussen, D. Nguyen, W. Geiger, R. Kedkiw. Smoke Simulation for Large Scale Phenomena. ACM Transactions on Graphics, 2003, 22(3):703-707
22 Kim B, Liu Y, Llama I. Flow Fixer: Using BFECC for Fluid Simulation. //Proceedings of Eurographics Workshop on Natural Phenomena, 2005
23 Dupont T.F, Liu Y. Back and forth error compensation and correction methods for semi-Lagrangian schemes with application to level set interface computations. Mathematics of Computation, 2007, 76(258):647-668
24 Crane K., LLAMAS I, TARIQ S. Real-time simulation and rendering of 3d fluids. Urbana-Champaign: University of Illinois, 2007
25 Selle A, Fedkiw R, Kim B. An unconditionally stable MacCormack method. Journal of Scientific Computing, 2008, 35(2-3): 350-371
26 H. Schechter, R. Bridson. Evolving Sub-Grid Turbulence for Smoke Animation. ACM SIGGRAPH Symposium On Computer Animation, 2008
27 Kun Zhou, Zhong Ren. Real-time Smoke Rendering Using Compensated Ray Marching. ACM SIGGRAPH, 2008, 27(3): 36:1-36:12
28 Yang Qing. Real-time Simulation of 3D Smoke Based on Navier-Stokes Equation. WSEAS Transactions On Computers, 2009, 8(1):103-112
29 Patrick Mullen, Keenan Crane. Energy-Preserving Integrators for Fluid Animation.ACM Trans on Graph. 2009, 28(3):38:1-38:8
30 Ding Wanning, Jiao Hongqiang. Real-time simulation of smoke. 2010Second International Conference on Computer Modeling and Simulation, 2010(3):128-131
31秦培煜,陈传波,吕泽华,等.基于物理模型的烟雾实时模拟.小型微型计算机系统,2007, 28(8):1486-1488
32湛永松,石民勇,费广正.基于流体力学方程的二维烟雾模拟.中国传媒大学学报, 2007, 14(1):68-72
33湛永松,杨明浩,石民勇,等.保持自然特征的烟雾快速生成系统.系统仿真学报, 2007, 19(19):4460-4463
34周永霞.基于物理的烟雾动画研究. [浙江大学博士论文], 2006:44-55
35 Yongxia Zhou, Xiehua Sun, Xiangyang Lan, et al. Fast Smoke Simulation of Moving Object. Computer Animation and Virtual Worlds, 2007, 18(4-5):455-461
36唐勇,李晓艳,吕梦雅,等. MacCormack方法优化烟雾模拟中Navier-Stokes方程对流项的求解.计算机辅助设计与图形学学报, 2010, 22(4):724-728
37 A. Treuille, A. McNamara, Z. Popovic,et al. Keyframe Control of Smoke Simulations. ACM Transactions on Graphics(TOG), 2003, 22(3):716-723
38 F. Raanan, L. Dani. Target-driven Smoke Animation. ACM Transactions on Graphics, 2004, 23(3):439-446
39 Frank Losasso, Frederic Gibou, Ronald Fedkiw. Simulation Water and Smoke with an Octree Data Structure. ACM SIGGRAPH, 2004, 23(3):457-462.
40 Bryan Feldman, James O'Brien, Bryan Klingner. Animating Gases with Hybrid Meshes. ACM Transactions on Graphics, 2005, 24(3):904-909.
41 Bryan Klingner, Bryan Feldman, Nuttapong Chentanez, et al. Fluid Animation with Dynamic Meshes. ACM Transactions on Graphics, 2006, 25(3): 820-825
42 Yoshinori Dobashi, Yasuhiro Matsuda, et al. A Fast Simulation Method Using Overlapping Grids for Interactions between Smoke and Rigid Objects. // EUROGRAPHICS, 2008, 27 (2): 477-486
43 T. Kim, N. Thurey, D. James, M. Gross. Wavelet Turbulence for Fluid Simulation. ACM Transactions On Graphics,2008, 27(3): 50:1-50:6
44 Jang Yoojin, lhm.Insung. Chemical Kinetics-assisted, Path-based Smoke Simulation. Computer Animation and Virtual Worlds, 2009, 20(2-3):247-256
45 Rice S O. Mathematical analysis of random noise // Selected Papers on Noise and Stochastic Process Dover Publish Inc . New York, 1954
46 Borgman L E. Ocean wave simulation for engineering design. J. W trway Hard. Div , ASCE, 1969, 95(4):557-583
47 Shinozuka M, Deotatis G. Simulation of stochastic processes by spectral representation. Applied Mechanics Reviews, 1991, 44:191-203
48 Yang W W, Chang T Y P, Chang C C. An efficient wind field simulation technique for bridges. Journal of Wind Engineering and Industrial Aerodynamics, 1997:67-68
49屈应辉,徐旭.大跨度悬索桥脉动风场的数值模拟.工业建筑, 2006, 36(增刊):398-402
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