Abstract
Advancements to the adaptive wavelet-collocation method over the last decade have opened up a number of new possible areas for active research. Volume penalization techniques allow complex immersed boundary conditions to be used with high efficiency for both internal and external flows. Anisotropic methods make it possible to use body-fitted meshes while still taking advantage of the dynamic adaptability properties wavelet-based methods provide. The parallelization of the approach has made it possible to perform large high-resolution simulations of detonation initiation and fluid instabilities to uncover new physical insights that would otherwise be difficult to discover. Other developments include space-time adaptive methods and nonreflecting boundary conditions. This article summarizes the work performed using the adaptive wavelet-collocation method developed by Vasilyev and coworkers over the past decade.
Highlights
Advancements to the adaptive wavelet-collocation method over the last decade have opened up a number of new possible areas for active research
Wavelet-Collocation Method (AWCM) that take it in new directions and generalize its application space
This review article focuses on the developments and discoveries made with the PDE solver originally developed by Vasilyev and Goldstein [2,3] in the early 2000s
Summary
Advancements to the adaptive wavelet-collocation method over the last decade have opened up a number of new possible areas for active research. Volume penalization techniques allow complex immersed boundary conditions to be used with high efficiency for both internal and external flows. Anisotropic methods make it possible to use body-fitted meshes while still taking advantage of the dynamic adaptability properties wavelet-based methods provide. Volume penalization techniques [4] have been developed that allow complex immersed boundaries to be placed inside of computational domains with ease. Multiple approaches were investigated in order to perform an asynchronous parallel wavelet transform, i.e., with only one synchronization of the buffer-zone They found that the most efficient solution is to skip the update stage of the wavelet transform over the entire computational domain.
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