Explicit Time-Stepping for Moving Meshes (Journal of Mathematical Study, 2015)
In order to move the nodes in a moving mesh method a time-stepping schemeis required which is ideally explicit and non-tangling (non-overtaking in one dimension(1-D)). Such a scheme is discussed in this paper, together with its drawbacks, andillustrated in 1-D in the context of a velocity-based Lagrangian conservation methodapplied to first order and second order examples which exhibit a regime change afternode compression. An implementation in multidimensions is also described in somedetail.
Keywords: PDEs; moving meshes; time stepping; no tangling.