A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion

Abstract Good mesh moving methods are always part of what makes moving-mesh good in computation flow problems with boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) arbitrary Lagrangian–Eulerian (ALE) enable mesh-resolution control near solid surfaces thus high-resolution representation boundary layers. Mesh based on linear elasticity mesh-Jacobian-based stiffening (MJBS) has been use ST ALE since 1992. In MJBS, objective is to stiffen smaller elements, which typically placed surfaces, more than larger ones, this accomplished by altering way we account for Jacobian transformation from element domain physical domain. computing motion between time levels $$t_n$$ tn $$t_{n+1}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">tn+1 linear-elasticity equations, most common option compute displacement configuration at . While works well problems, because method path-dependent, it involves cycle-to-cycle accumulated distortion. The back-cycle-based (BCBMM) method, introduced recently two versions, can remedy that. BCBMM, there no article, first time, present test computations BCBMM. We also introduce a version call “half-cycle-based moving” (HCBMM) that where or interface second half cycle consists just reversing steps want behave same way. detailed 2D 3D finite meshes, using case associated wing pitching. show all versions BCBMM perform well, distortion, HCBMM, reverses its half, behaves