论文标题
基于速度的移动网格虚拟元素方法
A Velocity-based Moving Mesh Virtual Element Method
论文作者
论文摘要
我们提出了一种基于速度的移动网格虚拟元素方法，用于涉及移动边界的PDE的数值解。虚拟元素方法用于计算一般多边形网格上的网格速度和保守的任意Lagrangian-Eulerian解决方案。该方法将线性有限元方法扩展到多边形网格结构，达到相同的准确性。在移动网格的背景下，虚拟元素方法的主要优势是可以在网格边缘插入节点的便捷性。提出了节点插入技术的演示，以表明可以简单地将运动多边形网格简单地适用于边界遇到固体对象或另一个移动边界的情况，而不会降低准确性的程度。
We present a velocity-based moving mesh virtual element method for the numerical solution of PDEs involving moving boundaries. The virtual element method is used for computing both the mesh velocity and a conservative Arbitrary Lagrangian-Eulerian solution transfer on general polygonal meshes. The approach extends the linear finite element method to polygonal mesh structures, achieving the same degree of accuracy. In the context of moving meshes, a major advantage of the virtual element approach is the ease with which nodes can be inserted on mesh edges. Demonstrations of node insertion techniques are presented to show that moving polygonal meshes can be simply adapted for situations where a boundary encounters a solid object or another moving boundary, without reduction in degree of accuracy.
