Boundary-conforming free-surface flow computations: Interface tracking for linear, higher-order and isogeometric finite elements
Boundary-conforming free-surface flow computations: Interface tracking for linear, higher-order and isogeometric finite elements
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DOI：
10.1016/j.cma.2017.08.022
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发表时间：
2017-08
影响因子：
7.2
通讯作者：
Florian Zwicke;S. Eusterholz;S. Elgeti
中科院分区：
文献类型：
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作者：
Florian Zwicke;S. Eusterholz;S. Elgeti
某些流动问题的模拟需要一种对自由流体表面进行建模的方法；例如，粘弹性模具膨胀或储罐中的流体晃动。在有限元环境中，除了许多其他选项外，这种类型的问题可以使用变形空间域/稳定时空（DSD/SST）公式的接口跟踪方法来处理。与这类方法相关的一个难题是确定边界处流体速度与边界网格节点位移之间的适当耦合机制。为了避免大的网格扭曲，一个目标是保持节点运动尽可能小；但仍然满足无侵彻边界条件。标准位移技术有全速、特定坐标方向上的速度和法向速度。在这项工作中，我们研究了如何将界面跟踪方法与等几何分析相结合以实现空间离散化。如果几何图形和解都使用足够阶数的NURBS基函数，则整个边界上的连续法向量和速度都是可用的。这种情况允许弱施加无穿透边界条件。我们将此选项与依赖于离散点强施加的替代方案进行比较。此外，我们还研究了流体方程、边界条件和内部控制点位置调整方程之间的几种耦合方法。
The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options, be dealt with using an interface-tracking approach with the Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. A difficult issue that is connected with this type of approach is the determination of a suitable coupling mechanism between the fluid velocity at the boundary and the displacement of the boundary mesh nodes. In order to avoid large mesh distortions, one goal is to keep the nodal movements as small as possible; but of course still compliant with the no-penetration boundary condition. Standard displacement techniques are full velocity, velocity in a specific coordinate direction, and velocity in normal direction. In this work, we investigate how the interface-tracking approach can be combined with isogeometric analysis for the spatial discretization. If NURBS basis functions of sufficient order are used for both the geometry and the solution, both a continuous normal vector as well as the velocity are available on the entire boundary. This circumstance allows the weak imposition of the no-penetration boundary condition. We compare this option with an alternative that relies on strong imposition at discrete points. Furthermore, we examine several coupling methods between the fluid equations, boundary conditions, and equations for the adjustment of interior control point positions.