Multiwavelet Troubled-Cell Indication: A Comparison of Utilizing Theory Versus Outlier Detection

摘要

Solutions to nonlinear hyperbolic PDEs develop discontinuities in time. The generation of spurious oscillations in such regions can be prevented by applying a limiter in the troubled zones. In [16, 18], two different multiwavelet troubled-cell indicators were introduced, one based on a parameter, the other using outlier detection. We present this comparison in order to begin to understand in which regime these tools are effective. In this paper, we investigate the effectiveness of a different detection scheme, based on the theoretical detection of troubled cells using multiwavelet approaches. It uses the cancelation property [6] and the theory about thresholding [8]. This technique was originally used for a multiwavelet-based adaptive strategy in combination with the DG method. However, we are specifically interested in its application for troubled-cell indication. In the troubled cells, the moment limiter is applied [11]. We demonstrate the performance of this new indicator and show that it works very well when very fine meshes are used (the asymptotic regime). For coarser meshes, it seems that the existing multiwavelet troubled-cell indicators perform better.