ITR: Collaborative Research on Multiresolution Adaptive Spectral Element Solvers for Atmospheric Fluid Dynamics

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This project will develop a multiresolution numerical methodology for solving the partial differential equations of fluid dynamics on the sphere, and apply it to practical atmospheric-flow simulations. Its starting point is the spectral-element method (SEM), which retains the spectral accuracy of spherical-harmonic transform methods, without the latter's problems near the poles. Observing that the spatial discretization via SEM and via multiwavelets (on the finest scale) are the same, the researchers will develop an adaptive multiresolution multiwavelet solver, and test it using standard atmospheric simulation benchmarks.Although it is well understood that atmospheric phenomena involve strong multiscale interactions, today there are no adaptive multiresolution solvers. The necessary mathematical tools that take the multiscale nature of the problem into account have appeared only recently, and form the foundation for this research. The success of this project will have a significant impact on both the speed and the accuracy of atmospheric simulations and weather prediction.