A New Adaptation Strategy for Multi-resolution Method

Adaptive mesh refinement (AMR) and wavelet-based multi-resolution technique, which refine the spatial resolution in regions of interest and coarsen the mesh in other regions, are widely used in scientific computing for higher computational efficiency. The key component of AMR and the multi-resolution method is the adaptation strategy including the regularity estimation. In this paper, a new adaptation strategy for AMR and the multi-resolution method is proposed. Different from AMR, which measures the function regularity based on an empirical gradient operator, and the multi-resolution method with complicated wavelet analysis, the new approach examines the solution smoothness based on the high-order TENO reconstruction (Fu et al. in J Comput Phys 305:333-359, 2016). The core idea is that the TENO scheme not only provides the reconstructed data at the cell interface for flux evaluation but also classifies the local flow scales as smooth or nonsmooth on the discretized mesh. Since the scale-separation procedure is achieved in the spectral and characteristic space, the new adaptation strategy is weakly problem-dependent. Moreover, the extra complexity due to the empirical gradient computing or the wavelet analysis is eliminated. Based on Harten's finite-volume multi-resolution method (Harten in J Comput Phys 115(2):319-338, 1994), a set of benchmark cases is simulated to validate the performance of the proposed method.

Automated summary

Adaptive mesh refinement (AMR) and wavelet-based multi-resolution technique are widely used in scientific computing for higher computational efficiency. This paper proposes a new adaptation strategy for AMR and the multi-resolution method, which examines the solution smoothness based on the high-order TENO reconstruction. The new strategy eliminates the complexity of empirical gradient computing or wavelet analysis and is weakly problem-dependent.