非结构动网格高精度计算格式的设计与实现

The Design and Implementation of the High-order Scheme on Unstructured Moving Grids

本文研究了动网格高精度算法在非结构网格上的设计和实现问题.动网格上的高精度重构方法为最近发展的变分重构方法;采用径向基插值方法实现了动网格的运动和变形.提出了在给定边界速度变化的时间历程和给定边界位置坐标变化的时间历程条件下,与变分重构方法和隐式时间推进相适应的高精度的动网格几何量计算方案.数值算例的计算结果显示,高阶变分重构方法在动网格上有较高的计算精度,而且相对二阶方法展现出了明显的优势.

The design and implementation of the high-order scheme on unstructured moving grids have been researched in this paper.The high-order reconstruction method on moving grids is the newly developed variational reconstruction method.The radial basis function interpolation method is used for mesh deformation.In this paper,the high-accuracy mesh movement algorithm adapted with the variational reconstruction and the implicit time integration is developed for two types of boundary movement:The given boundary velocity and the given boundary point coordinates.Numerical results indicate the high accuracy of the high-order variational reconstruction method on moving grids,and show the advantage of the highorder scheme over the second-order schemes.