Mesh Moving Methods in Flow Computations with the Space-Time and Arbitrary Lagrangian-Eulerian Methods

A good mesh moving method is an important part of flow computations with moving-mesh methods like the space–time (ST) and Arbitrary Lagrangian–Eulerian (ALE) methods. With a good mesh moving method, we can decrease the remeshing frequency even when the fluid–solid and fluid–fluid interfaces undergo large displacements, decrease the element distortion in parts of the flow domain where we care about the solution accuracy more, and maintain the quality of the boundary layer meshes near the fluid–solid interfaces as the mesh moves to follow those interfaces. Since 1990, quite a few good mesh moving methods have been developed for use with the ST computational methods, from the mesh Jacobian-based stiffening to a mesh moving method based on fiber-reinforced hyperelasticity to a linear-elasticity mesh moving method with no cycle-to-cycle accumulated distortion. These methods have been used in computation of many complex flow problems in the categories of fluid–particle interaction, fluid–structure interaction, and more generally, moving boundaries and interfaces. The computations were with both the ST and ALE methods. We provide an overview of these methods and present examples of the computations performed.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.