Balanced Monitoring of Flow Phenomena in Moving Mesh Methods (Communications in Computational Physics, 2010)
Adaptive moving mesh research usually focuses either on analytical derivationsfor prescribed solutions or on pragmatic solvers with challenging physical applications.In the latter case, the monitor functions that steer mesh adaptation are oftendefined in an ad-hoc way. In this paper we generalize our previously used monitorfunction to a balanced sum of any number of monitor components. This avoidsthe trial-and-error parameter fine-tuning that is often used in monitor functions. Thekey reason for the new balancing method is that the ratio between the maximum andaverage value of a monitor component should ideally be equal for all components.Vorticity as a monitor component is a good motivating example for this. Entropy alsoturns out to be a very informative monitor component. We incorporate the monitorfunction in an adaptive moving mesh higher-order finite volume solver with HLLCfluxes, which is suitable for nonlinear hyperbolic systems of conservation laws. Whenapplied to compressible gas flow it produces very sharp results for shocks and otherdiscontinuities. Moreover, it captures small instabilities (Richtmyer-Meshkov, Kelvin-Helmholtz).Thus showing the rich nature of the example problems and the effectivenessof the new monitor balancing.