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一种基于多松弛LBM模型的边界条件改进自由表面流体模拟方法

A Free Surface Fluid Simulation Method with Improved Boundary ConditionsBased on a Multi-Relaxation Model LBM

  • 摘要: 可视化流体仿真是计算机图形学的重要研究方向. 其中基于格子玻尔兹曼方法(LBM)的自由表面流体以其准确性和高效性受到了广泛关注. 针对现有方法在稳定性、流体细节捕捉、时间效率提升和边界处理等方面存在的问题, 文中首先提出了基于自适应粘性的多松弛模型的自由表面LBM流体模拟方法, 相比单松弛模型可捕捉更多的流体细节; 其次, 针对现有自适应时间步长方法过度缩小时间步长的问题进行优化, 提出了灵活高效的时间步长缩放策略, 提升了计算效率; 最后, 为解决移动障碍物表面流体附着问题, 改进了自由滑移边界条件和自由表面法向计算方法, 提升了流体与固体交互精度. 实验结果表明, 提出的基于自适应粘性的多松弛模型能保持90%以上的体积守恒率; 提出的自适应时间步长优化方法较对比方法在精度不变情况下提升了7.25%~25.85%的效率; 改进的边界条件使障碍物与流体交互更符合物理规律. 综上所述, 文中提出的自由表面流体模拟方法相较于对比方法具有精度和计算效率优势, 对推动LBM模型的可视化仿真应用具有积极意义.

     

    Abstract: Visual fluid simulation is an important research direction in computer graphics. Among them, free surface fluid based on the lattice Boltzmann method (LBM) has attracted widespread attention for its accuracy and efficiency. In view of the problems of existing methods in stability, fluid detail capture, time efficiency improvement and boundary processing, this paper first proposes a free surface LBM fluid simulation method based on a multi-relaxation model of adaptive viscosity, which can capture more fluid details than the single relaxation model; secondly, the problem of excessive time step reduction in the existing adaptive time step method is optimized, and a flexible and efficient time step scaling strategy is proposed to improve the computational efficiency; finally, in order to solve the problem of fluid attachment on the surface of moving obstacles, the free slip boundary conditions and free surface normal calculation method are improved to improve the accuracy of fluid-solid interaction. Experimental results show that the proposed multi-relaxation model based on adaptive viscosity can maintain a volume conservation rate of more than 90%; the proposed adaptive time step optimization method improves the efficiency by 7.25%~25.85% compared with the comparison method without changing the accuracy; the improved boundary conditions make the interaction between obstacles and fluids more in line with physical laws. In summary, The free surface fluid simulation method proposed in this paper has advantages in accuracy and computational efficiency compared with the comparative method, which has positive significance for promoting the visualization simulation application of LBM.

     

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