Good mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels \(t_n\) and \(t_{n+1}\) with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at \(t_n\). While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.

好的网格移动方法始终是使移动网格方法在计算具有移动边界和界面（包括流固耦合）的流动问题方面表现出色的一部分。诸如时空（ST）和任意拉格朗日-欧拉（ALE）方法之类的移动网格方法可以在固体表面附近进行网格分辨率控制，从而实现边界层的高分辨率表示。自1992年以来，ST和ALE方法就开始使用基于线性弹性和基于雅可比网格的加筋（MJBS）的网格移动。在MJBS中，其目的是使较小的元素（通常位于实体表面附近）变硬，这要比更大的方法要大，而这是通过改变我们计算从元素域到物理域的雅可比变换的方式来实现的。\（t_n \）和\（t_ {n + 1} \）与线性弹性方程式，最常见的选择是根据\（t_n \）处的配置计算位移。尽管此选项对大多数问题都适用，但由于该方法与路径有关，因此涉及逐周期累积的网格变形。最近引入了两个版本的基于循环的网格移动（BCBMM）方法可以对此进行补救。在BCBMM中，没有逐周期累积的失真。在本文中，我们首次使用BCBMM提出了网格移动测试计算。我们还引入了一种称为“基于半周期的网格移动”（HCBMM）方法的版本，该方法用于在循环的后半部分中边界或界面运动仅需反转前半部分中的步骤进行计算。我们希望网格物体的行为相同。我们使用与机翼俯仰相关的网格运动作为测试案例，介绍了有限元网格的详细2D和3D测试计算。