Adaptive moving mesh research usually focuses either on analytical deriva-tions for prescribed solutions or on pragmatic solvers with challenging physical appli-cations. In the latter case, the monitor functions that ...Adaptive moving mesh research usually focuses either on analytical deriva-tions for prescribed solutions or on pragmatic solvers with challenging physical appli-cations. 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 moni-tor function 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 effective-ness of the new monitor balancing.展开更多
基金The first author performs his research in the project‘Adaptive moving mesh methods for higher-dimensional nonlinear hyperbolic conservation laws’,funded by the Netherlands Organisation for Scientific Research(NWO)under project number 613.002.055.
文摘Adaptive moving mesh research usually focuses either on analytical deriva-tions for prescribed solutions or on pragmatic solvers with challenging physical appli-cations. 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 moni-tor function 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 effective-ness of the new monitor balancing.
