Abstract
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.
Highlights
Mesh moving based on linear elasticity and mesh-Jacobianbased stiffening (MJBS) [1,2,3] has been in use with moving- B Kenji TakizawaComputational Mechanics (2021) 67:413–434 to the physical domain
To show how the back-cycle-based mesh moving (BCBMM) and half-cyclebased mesh moving” (HCBMM) perform, we present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching
In the BCBMM, in computing the mesh motion between time levels tn and tn+1 with the linear-elasticity equations, in any cycle, the mesh motion is computed from the configurations in the first cycle
Summary
In computing the mesh motion between time levels tn and tn+1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at tn While this option works well for most problems, because the method is pathdependent, it involves cycle-to-cycle accumulated mesh distortion. Moving the mesh based on large-deformation mechanics equations, instead of the linear-elasticity equations, would be one good way of addressing the issue This mesh moving approach has been in use in FSI and MBI computations, such as those reported in [4,5,6,7,8]. The Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) [12] was introduced for computation of MBI problems that involve both fluid–solid interfaces that can be accurately tracked with a moving-mesh method and fluid–fluid interfaces that are too complex or unsteady to be tracked. In the FSITICT, we track the interface we can with a moving mesh, and capture over that moving mesh the interfaces we cannot track, the interfaces where we need to have an actual contact between the solid surfaces
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