Time-dependent partial differential equations are indispensable in scientific and engineering research, where they are used to model physical phenomena such as fluid flow and combustion. Moving mesh numerical solution methods have proven to be particularly well-suited to compute solutions to such problems which change non-uniformly over time. Computer visualization of moving mesh methods is an ...

In this paper we describe an adaptive moving mesh technique and its application to the 2D Euler equations. The adaptive mesh is derived from the minimization of a mesh-energy integral. A robust and efficient monitor function with a time-dependent, automatically chosen, adaptivity parameter is used to track individual features of the physical solutions, such as shocks and emerging instabilities....