论文标题
流体模拟的杂种拉格朗日/欧拉岛的隔线对流和投影方法
A Hybrid Lagrangian/Eulerian Collocated Advection and Projection Method for Fluid Simulation
论文作者
论文摘要
我们提出了一种杂交粒子/网格方法，用于模拟与速度网格上的不可压缩流体。我们互换使用运输数量的粒子和网格表示来平衡效率和准确性。一种新型的落后半拉格朗日方法得出了提高基于网格的对流的准确性。我们的方法利用与汉堡方程解决方案相关的隐式公式。我们使用由$ C^1 $连续网格插值启用的牛顿方法来求解该方程。我们在相处而不是交错的网格上实现了不可压缩性。我们的投影技术是变异的，设计用于B-Spline插值的常规网格，其中多静脉插值用于速度和多线性插值以用于压力。尽管我们使用了常规网格，但我们扩展了变分技术，以允许对Dirichlet和自由表面边界条件的不规则流动域进行切割定义。
We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. We interchangeably use particle and grid representations of transported quantities to balance efficiency and accuracy. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of Burgers' equation. We solve this equation using Newton's method enabled by $C^1$ continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B-spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut-cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.
