基于波动方程的三维水体仿真模拟
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摘要
如何有效模拟3D水体表面的动态传播过程一直是数字流域的热点问题。从基于流体力学原理的简化方程出发,该方程与地震波动方程具有相似性,同时构建了对应的有限差分数值计算格式,并推导了稳定性条件。以较为剧烈变化的水面为初始边界条件,通过波动方程的数值迭代,构建了连续的、真实的、动态的水体传播场景。数值计算表明,基于波动方程水波模拟方法的模拟效果符合水波传播的物理规律,可以再现水体表面的动态变化过程,且计算效率较高。
How to effectively simulate the 3D water surface's dynamic propagating process is the hot problem in the domain of numerical flow.The paper starts from a simplified equation based on fluid mechanics principle,and verifies the similarity with the seismic wave equation,and constructs a corresponding finite difference numerical computational format and its stable condition.We take a dramatic ally changing water surface as our initial boundary condition.With the numerical iteration of the wave equation,we construct continuous,real,dynamic water propagating scenarios.The numerical computation results show that,the proposed method's simulating effect is in accordance with the laws of physics of wave propagation,and the surface water's dynamic changes can reappear with high computational efficiency.
How to effectively simulate the 3D water surface's dynamic propagating process is the hot problem in the domain of numerical flow.The paper starts from a simplified equation based on fluid mechanics principle,and verifies the similarity with the seismic wave equation,and constructs a corresponding finite difference numerical computational format and its stable condition.We take a dramatic ally changing water surface as our initial boundary condition.With the numerical iteration of the wave equation,we construct continuous,real,dynamic water propagating scenarios.The numerical computation results show that,the proposed method's simulating effect is in accordance with the laws of physics of wave propagation,and the surface water's dynamic changes can reappear with high computational efficiency.
引文
[1]何希平,朱庆生.运行体的水波生成与扩散模拟算法[J].计算机仿真,2005,22(9):174-181.
[2]陈路,桑楠,熊光.水波现象的光学模型及其三维仿真研究与应用[J].计算机应用,2005,25(1):2459-2461.
[3]宋利,周源华,周军.基于Fourier合成技术的水波动画[J].计算机工程与应用,2002,38(6):10-11.
[4]杨怀平,胡事民,孙家广.一种实现水波动画的新算法[J].计算机学报,2002,25(6):612-617.
[5]鄢来斌,李思昆,张秀山.虚拟海战场景中的海浪实时建模与绘制技术研究[J].计算机研究与发展,2001,38(5):268-273.
[6]Premoze S,Ashikhmin M.Rendering natural waters[J].Computer Graphics Forum,2001,20(4):612-617.
[7]刘东海,崔广涛,钟登华,等.泄洪雾化的粒子系统模拟及三维可视化[J].水利学报,2005,36(10):1194-1198.
[8]lwasaki K,Dobashi Y,Nishita T.A fast rendering method for refractive and reflective caustics due to water surfaces[J].Computer Graphics Forum,2003,22(3):601-609.
[9]庞明勇.基于离散模型的二维水波实时动态模拟方法[J].水利学报,2007,38(11):1358-1363.
[10]陈可洋.一种实用的水波数值模拟方法[J].工程地质计算机应用,2010,58(2):38-42.
[11]丁振,芮小平,刘真余,等.基于中心差分法的理想水体三维运动效果的模拟[J].中国科学院研究生院学报,2013,30(1):33-39.
[12]陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232-236.
[13]陈可洋.地震波叠后深度偏移方法及其速度敏感性分析[J].工程地质计算机应用,2010,58(2):10-14.
[14]陈可洋.复杂介质高精度地震波正演和叠后逆时深度偏移[J].石油工业计算机应用,2010,65(3):7-9.
[15]陈可洋.地震波数值模拟中差分近似的各向异性分析[J].石油物探,2010,49(1):19-22.
[2]陈路,桑楠,熊光.水波现象的光学模型及其三维仿真研究与应用[J].计算机应用,2005,25(1):2459-2461.
[3]宋利,周源华,周军.基于Fourier合成技术的水波动画[J].计算机工程与应用,2002,38(6):10-11.
[4]杨怀平,胡事民,孙家广.一种实现水波动画的新算法[J].计算机学报,2002,25(6):612-617.
[5]鄢来斌,李思昆,张秀山.虚拟海战场景中的海浪实时建模与绘制技术研究[J].计算机研究与发展,2001,38(5):268-273.
[6]Premoze S,Ashikhmin M.Rendering natural waters[J].Computer Graphics Forum,2001,20(4):612-617.
[7]刘东海,崔广涛,钟登华,等.泄洪雾化的粒子系统模拟及三维可视化[J].水利学报,2005,36(10):1194-1198.
[8]lwasaki K,Dobashi Y,Nishita T.A fast rendering method for refractive and reflective caustics due to water surfaces[J].Computer Graphics Forum,2003,22(3):601-609.
[9]庞明勇.基于离散模型的二维水波实时动态模拟方法[J].水利学报,2007,38(11):1358-1363.
[10]陈可洋.一种实用的水波数值模拟方法[J].工程地质计算机应用,2010,58(2):38-42.
[11]丁振,芮小平,刘真余,等.基于中心差分法的理想水体三维运动效果的模拟[J].中国科学院研究生院学报,2013,30(1):33-39.
[12]陈可洋.标量声波波动方程高阶交错网格有限差分法[J].中国海上油气,2009,21(4):232-236.
[13]陈可洋.地震波叠后深度偏移方法及其速度敏感性分析[J].工程地质计算机应用,2010,58(2):10-14.
[14]陈可洋.复杂介质高精度地震波正演和叠后逆时深度偏移[J].石油工业计算机应用,2010,65(3):7-9.
[15]陈可洋.地震波数值模拟中差分近似的各向异性分析[J].石油物探,2010,49(1):19-22.
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