Abstract
This paper reviews how dynamically adaptive wavelet methods can be designed to simulate atmosphere and ocean dynamics in both flat and spherical geometries. We highlight the special features that these models must have in order to be valid for climate modelling applications. These include exact mass conservation and various mimetic properties that ensure the solutions remain physically realistic, even in the under-resolved conditions typical of climate models. Particular attention is paid to the implementation of complex topography in adaptive models. Using wavetrisk as an example, we explain in detail how to build a semi-realistic global atmosphere or ocean model of interest to the geophysical community. We end with a discussion of the challenges that remain to developing a realistic dynamically adaptive atmosphere or ocean climate models. These include scale-aware subgrid scale parameterizations of physical processes, such as clouds. Although we focus on adaptive wavelet methods, many of the topics we discuss are relevant for adaptive mesh refinement (AMR).
Highlights
This Special Issue of Fluids highlights a range of applications of wavelet-based techniques to problems in fluid dynamics, both for data analysis and for the numerical solution of the Navier–Stokes or other fluid equations
We focus on climate models, and especially global models on the sphere, many of these features apply to regional models on shorter time scales, as well as to adaptive mesh refinement (AMR) implementations
This review has outlined the essential and desirable features a dynamically adaptive wavelet method must have in order to be practically useful for ocean and atmosphere modelling
Summary
This Special Issue of Fluids highlights a range of applications of wavelet-based techniques to problems in fluid dynamics, both for data analysis and for the numerical solution of the Navier–Stokes or other fluid equations. Adaptive multiscale wavelet collocation methods are mostly limited to engineering applications, especially high Reynolds number incompressible and compressible flows This is surprising since perhaps the most challenging and important applications of computational fluid dynamics are the Earth systems models of the ocean and atmosphere. They demonstrate that adaptive wavelet collocation models can achieve good parallel performance on standard geophysical test cases In addition to these fundamental issues related to numerical modelling of geophysical flows, in Section 5 we briefly summarize two complementary wavelet-based techniques that can be used to improve the performance of adaptive multiscale wavelet-based methods: local time stepping and adaptive multigrid solvers for elliptic equations.
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