Adaptive multi-scale shallow flow model: a wavelet-based formulation

This work outlines the use of wavelet bases to re-formulate a finite volume (FV) local solution of the shallow water equations (SWEs), so as to achieve mesh adaptivity via local compression and truncation of the numerical solution’s details across successive resolution scales with reference to a single threshold error set by the user. The wavelet bases naturally lead to a scalable FV formulation and how they can readily be exploited to achieve adaptive mesh-resolution selection: up-scaling and/or down- scaling by means of the local solutions’ data (i.e. both flow variables and terrain). Our results show a notable promise in using wavelets as a basis for future flood models to achieve conservative and more autonomous simulation at a wide range of length-scales.