一类二阶守恒单调重映算法

在大变形流体力学问题的数值模拟中，经常会涉及到计算网格的重分。基于不同网格的物理量传递便是所谓的重映技术。重映算法是任意拉格朗日一欧拉方法的重要组成部分，本文描述了一类适用于任意网格的二阶守恒单调重映算法。该算法分为网格内物理量的多项式重构、近似积分计算、物理量的单调修正三个部分。本文采用了最小二乘法的思想构造了网格内物理量的梯度，并且通过对物理量的单调修正，保证了算法的精度和单调性。该算法计算公共表面上的网格间质量的改变，所以可以在任意网格上使用。通过一系列数值算例验证了该算法，并说明本文给出的算法是有效可行的。

A Kind of Second-order Conservative Monotone Remapping Algorithms

In the research of simulation for problems with large di stortion in fluid dynamics, it is often required to reconstruct the computationa l meshes. The technique transferring physical quantities between the two computa tional meshes is called as rezoning (remapping). An accurate remapping algorithm is an essential component of arbitrary Lagrangian-Eulerian (ALE) methods. This paper describes an efficient, second-order accurate, monotone remapping algori thm developed by structured and unstructured computational meshes. The remapping algorithm is based on three parts:reconstruction, approximate integration and m onotone preservation. The algorithm is accurate and monotone by using the least squares methods to reconstruct the physical quantity gradients in each cell and to apply monotone preservation. Based on estimating the mass exchanged between c ells at their common interface, the algorithm is equally applicable to structure d and unstructured grids. Through testing a set of reliable numerical examples, it shows that the algorithm is effective.