多边形交错网格的守恒重映算法

提出基于细分和数值积分思想的一种离散的守恒重映方法——质点重映方法.密度分布可采用一阶精度的分片常数分布,或二阶精度的分片线性分布.分片线性密度分布函数采用面平均方法构造.重映过程中,借助四边形辅助网格,实现了交错网格节点量的重映.质点重映方法既适用于结构网格,也适用于非结构网格,且不要求新旧网格之间一一对应.数值结果表明,一阶精度重映算法健壮性好,但会产生较大的扩散效应;二阶精度重映算法可较好地保持密度分布的特性,但存在单调性问题.为改善二阶精度重映方法单调性,将结构网格质量守恒调整算法推广到非结构网格上,以限制新网格的质量密度.给出了一些重映的例子,并进行了误差分析.

A Conservative Remapping Algorithm for Polygonal Staggered Meshes

A discrete conservative remapping algorithm based upon refinement and numerical integrals, named particle remapping algorithm, is presented. The mass density distribution is chosen as either a piecewise constant with first-order accuracy or a piecewise linear distribution with second-order accuracy. It results in a first-order and a second-order algorithm. The density gradient is evaluated by an area average method with a piecewise linear distribution. On a staggered mesh, in which velocity is vertex-centered, an auxiliary mesh is introduced, and the velocity is remapped. The particle remapping algorithm can be applied to a structured or an unstructured mesh. It does not require a one-to-one mapping between the old and the new meshes. Numerical results show that the first-order algorithm is robust but has an excessive diffusion. The second-order one is better in shape- preservation but violates the monotonicity sometimes. To improve the monotonicity, a conservative mass repair algorithm for structured grids is extended to unstructured grids preserving upper and lower bounds of the density. Several remapping results are presented and the errors are analyzed.