目的 基于物理的流体动画模拟是计算机图形学领域中的研究热点,针对实际应用中仍难以实现大规模流体场景的真实感与实时模拟,提出了基于shallow water方程的物理模拟方法。方法 首先,给出shallow water方程的稳定欧拉数值求解方法,解决模拟过程中存在的毛刺、陡坡水滴斑点等数值求解的不稳定性问题;其次,提出刚体和粒子系统与流体高度场的稳定耦合模型,实现双向固流耦合和流体表面细节的真实感模拟;最后,设计高度场的多精度网格算法以及粒子的隔点采样方法,加速大规模流体的物理模拟计算。结果 实验结果表明,本文方法解决了传统欧拉方法求解shallow water方程的流体模拟过程中存在的不稳定和计算复杂等问题,在300×300网格分辨率和2.2×10⁴粒子数的规模下,达到了20帧/s的实时模拟速度。结论 本文算法具有良好的高效性和稳定性,适用于电子游戏和视景仿真等实时应用领域中的大规模流体场景的真实感模拟。

Objective Physically based fluid animation is an advanced research hotspot in the computer graphics area. However, the realistic and real-time simulation of large-scale fluid simulation is still difficult to handle using current methods. To solve these problems, this study proposes a novel physically based method based on shallow water equation. Method First, to deal with the instability problems of numerical solution, such as blur and water spot artificial effects, our method proposes to solve shallow water equation using a stable Euler numerical method. Second, we propose a stable model of coupling fluid height field with rigid body and particle system; thus, a two-way fluid-solid coupling and small-scale features can be realistically simulated. Third, to achieve real-time simulation, we design a multiresolution grid algorithm and an interval particle sampling algorithm to accelerate the entire simulation process. Result Experimental results demonstrate that the proposed method can solve the instability and calculation complex problems and achieve 20 fps in the configuration of 300×300 grid resolution and 22K fluid particles. Conclusion The proposed method is stable and efficient and suits the realistic simulation of large-scale fluid for real-time applications, such as computer games and 3D vision simulation.