A Study of Moving Mesh Generation with Mathematical Adaption

Exploring Mesh Generation and Motion with Mathematical Adaption

Abstract

In this analysis we will focus on the refining method and present a way to transfer the mesh nodes. Typically it is possible to use the r-refining method to evaluate either the mesh point position or the pace. The mesh can be translated from a theoretical background to the physical space in which the PDE is to be solved and then the rate of change in the time of this mapping can be considered as the speed of the mesh. Every computing node thus has a specific speed, with which it travels, from which the mesh can be progressed in time. This speed can be interpreted as a function of the physical space variable since there is an implicit mapping between machine- and physical areas. Therefore, we need a method to produce this speed and in this step a monitor function is used to create it. This will help to monitor the relative density and hence the degree of mesh adaptation of the mesh points in the physical domain. The way we produce these mesh speeds depends on preserving the Monitor Function Concept in time, which can be used to induce a mesh motion. An Eulerian conservation law can be extracted from this concept to ensure that the mesh speed is obtainable from the display. This conservation legislation for the mesh motions is used to achieve a unique mesh speed in combination with a curl condition that determines the rotating properties of the mesh. In conjunction with the curl conditions, the conservation law then shows that the mesh-speed potentials can be derived from an elliptic equation.