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流体动画模拟的真实感与实时性一直是流体模拟研究中的热点. 针对在复杂地形场景中不稳定的流体表面运动现象, 本文提出一种基于地形差异的自适应流体速度控制力, 建立了稳定性光滑粒子流体动力学方法以求解浅水方程数值模型. 首先, 将模拟域从三维降至二维表面来降低计算量, 通过粒子的密度大小表示其水深高度值; 其次, 采用变长光滑搜索半径, 确保搜索邻域内的粒子数目稳定在固定范围内, 提高模拟精度; 最后引入一种基于地形差异的自适应流体速度控制力, 根据粒子密度大小的实时变化来确定计算速度控制力的地形研究范围, 通过插值计算粒子运动前后时间步所处地形位置的差异来修正粒子的速度和位置. 本文使用屏幕空间流体渲染方法对流体表面进行绘制, 避免了表面网格的提取与重建, 流体的运动数值计算和渲染均被加载到GPU上并行化执行, 实验结果表明在达到实时交互级别的同时, 本文方法有效地改善了在复杂地形场景中流体表面的不稳定运动现象, 同时流体模拟过程中密度与压强的分布均匀.The reality and real-time performance have always been the research hot-point of fluid simulation. Aiming at the unstable fluid surface motion in the scenes with complex terrain, in this paper, we propose an adaptive fluid velocity control force calculation model based on terrain difference, and a stable SPH numerical model for solving the shallow water equations is established. In this proposed numerical model, firstly we reduce the simulation domain from three-dimensional space to two-dimensional surface for reducing calculation quantity, and the water depth is represented by the density of particles at the meantime. Secondly, to ensure that the number of neighborhood particles is stable within a fixed range and to improve the accuracy of simulation, we apply a variable smoothing length to our numerical model. Then, an adaptive fluid velocity control force calculation model is introduced based on terrain difference, in which the velocity and position of particles are corrected by calculating the terrain difference caused by particle movement between each time step. The coordinates on terrain used for the calculation of terrain difference are dynamically chosen by the density of the particles. To improve the real-time performance of simulation, a screen space fluid rendering method is used to refrain the extraction and reconstruction of fluid surface. The numerical calculation and fluid surface rendering both load on the GPU for parallel execution. The simulation result shows that the proposed method can effectively improve the unstable fluid surface movement in scenes with complex terrain while reaching a real-time interaction level. The density and pressure are evenly distributed during the simulation.
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Keywords:
- smoothed particle hydrodynamics/
- shallow water equations/
- parallel computing/
- complex terrain
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物理量 值 单位 粒子半径 $ r $ 0.5 m 时间步长 $ \Delta t $ 0.02 s 初始粒子间距 $ {r_0} $ 1 m 初始搜索半径 $ {h_0} $ 2.66 m 静密度 $ {\rho _0} $ 1000 kg/${{\rm{m}}^3}$ 粒子质量 $ m $ 1000 kg 气体常数 $ k $ 10 — 黏度系数 $ \mu $ 0.1 — 
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点位 模拟水深/m 实测水深/m 相对误差/% A 1.29 1.43 9.79 B 1.51 1.65 8.48 C 1.97 1.92 2.60 D 1.50 1.40 7.14 下载:
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