Peskin Adele P, Hardin Gary R
National Institute of Standards and Technology, Boulder, CO 80303.
J Res Natl Inst Stand Technol. 1998 Jan-Feb;103(1):77-91. doi: 10.6028/jres.103.004. Epub 1998 Feb 1.
We present a new numerical technique for modeling the flow around multiple objects moving in a fluid. The method tracks the dynamic interaction between each particle and the fluid. The movements of the fluid and the object are directly coupled. A background mesh is designed to fit the geometry of the overall domain. The mesh is designed independently of the presence of the particles except in terms of how fine it must be to track particles of a given size. Each particle is represented by a geometric figure that describes its boundary. This figure overlies the mesh. Nodes are added to the mesh where the particle boundaries intersect the background mesh, increasing the number of nodes contained in each element whose boundary is intersected. These additional nodes are then used to describe and track the particle in the numerical scheme. Appropriate element shape functions are defined to approximate the solution on the elements with extra nodes. The particles are moved through the mesh by moving only the overlying nodes defining the particles. The regular finite element grid remains unchanged. In this method, the mesh does not distort as the particles move. Instead, only the placement of particle-defining nodes changes as the particles move. Element shape functions are updated as the nodes move through the elements. This method is especially suited for models of moderate numbers of moderate-size particles, where the details of the fluid-particle coupling are important. Both the complications of creating finite element meshes around appreciable numbers of particles, and extensive remeshing upon movement of the particles are simplified in this method.
我们提出了一种新的数值技术，用于对在流体中移动的多个物体周围的流动进行建模。该方法跟踪每个粒子与流体之间的动态相互作用。流体和物体的运动直接耦合。设计了一个背景网格以适应整个域的几何形状。除了为了跟踪给定大小的粒子需要多精细之外，网格的设计与粒子的存在无关。每个粒子由描述其边界的几何图形表示。该图形覆盖在网格上。在粒子边界与背景网格相交的地方向网格添加节点，从而增加其边界被相交的每个单元中包含的节点数量。然后在数值方案中使用这些额外的节点来描述和跟踪粒子。定义适当的单元形状函数以近似具有额外节点的单元上的解。通过仅移动定义粒子的覆盖节点，使粒子在网格中移动。常规的有限元网格保持不变。在这种方法中，随着粒子移动，网格不会变形。相反，随着粒子移动，仅定义粒子的节点的位置会改变。当节点在单元中移动时，单元形状函数会更新。这种方法特别适用于中等数量的中等大小粒子的模型，其中流体 - 粒子耦合的细节很重要。在这种方法中，围绕大量粒子创建有限元网格的复杂性以及粒子移动时的广泛重新网格化都得到了简化。
