Divergence-free and boundary-respecting velocity interpolation using stream functions
Divergence-free and boundary-respecting velocity interpolation using stream functions
复制标题
使用流函数进行无散且尊重边界的速度插值
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Christopher Batty
中科院分区：
文献类型：
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作者：
Jumyung Chang;V. C. Azevedo;Christopher Batty
在基于网格的流体模拟中，每个单元的离散不可压缩性由压力投影来强制执行。然而，逐点的速度构建的离散速度样本从交错网格插值不是真正的发散自由，导致非物理的局部体积变化，表现为颗粒扩散和聚类。我们提出了一种新的速度插值方法，使用流函数在二维中产生解析的无发散速度场。一个简单的微积分恒等式保证了所得到的场是无发散的：任何向量场的旋度都产生一个无发散的向量场。此外，我们的方法适用于切割单元格网格，以产生严格遵守固体边界条件的场。因此，不会在流体粒子和实体之间创建人工间隙，并且流体粒子不会侵入实体区域。
In grid-based fluid simulation, discrete incompressibility of each cell is enforced by the pressure projection. However, pointwise velocities constructed by interpolating the discrete velocity samples from the staggered grid are not truly divergence-free, resulting in unphysical local volume changes that manifests as particle spreading and clustering. We present a new velocity interpolation method that produces analytically divergence-free velocity fields in 2D using a stream function. The resulting fields are guaranteed to be divergence-free by a simple calculus identity: the curl of any vector field yields a divergence-free vector field. Furthermore, our method works on cut cell grids to produce fields that strictly obey solid boundary conditions. Therefore, no artificial gaps are created between fluid particles and solids, and fluid particles do not trespass into solid regions.