大时间步长下体积守恒的实时水体模拟  

Real-Time Simulation of Water with Volume Conservation in Large Time Step

作　　者：朱奎鑫 盖孟 赖舜男[2] ZHU Kui-xin;GAI Meng;LAI Shun-nan(Peking University Shenzhen Graduate School,Shenzhen Guangdong 518055,China;School of Electronics Engineering and Computer Science,Peking University,Beijing 100871,China;Beijing Engineering Technology Research Center of Virtual Simulation and Visualization,Peking University,Beijing 100871,China)

机构地区：[1]北京大学深圳研究生院,广东深圳518055 [2]北京大学信息科学技术学院,北京100871 [3]北京大学北京市虚拟仿真与可视化工程中心,北京100871

出　　处：《图学学报》2019年第4期725-732,共8页Journal of Graphics

基　　金：国家重点研发计划课题(2017YFB1002705);国家自然基金面上项目(61872398,61632003);装备预研基金项目(315050501)

摘　　要：基于物理的流体仿真可以真实地捕捉水的运动,一种常用的实时模拟方法是基于二维浅水方程进行水体仿真。首先介绍了二维浅水方程,并提出一种新的求解方法,通过一种体积守恒的隐式半拉格朗日方法进行计算,在保持稳定的同时允许较大的时间步长,然后额外增加修正步以保证计算过程中体积守恒。此外提出了一种基于动量守恒的流固耦合方法,可以实时地模拟出较为真实的水体,并且保证了水体体积始终守恒,效果良好。Physics-based fluid simulation can capture the movement of water.A common real-time simulation method is based on two-dimensional shallow water equation.Firstly,we introduce the two-dimensional shallow water equation,and then propose a new solution method,which is calculated by an implicit semi-Lagrangian method with volume conservation.This method allows a large time step while maintaining stability.Finally,we add additional correction steps to ensure volume conservation in the calculation process.In addition,a fluid solid coupling method based on momentum conservation is proposed,which works well.The model can simulate water more realistically in real time and ensure that the water volume is always conserved.

关 键 词：浅水方程 半拉格朗日 体积守恒 大时间步长 流固耦合 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]