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This is the PhD dissertation of Yassine Tissaoui successfully defended on July 9, 2024 at NJIT in mechanical engineering. The co-main advisors for the dissertation are Simone Marras (NJIT) and Stephen Guimond (Hampton University). The increasing frequency and intensity of tropical cyclones (TCs) due to climate change pose significant challenges for forecasting and mitigating their impacts. Despite advancements, accurately predicting TC rapid intensification (RI) remains a challenge. Large eddy simulation (LES) allows for explicitly resolving the large eddies involved in TC turbulence, thus providing an avenue for studying the mechanisms behind their intensification and RI. LES of a full tropical cyclone is very computationally expensive and its accuracy will depend on both explicit and implicit dissipation within an atmospheric model. This dissertation presents two novel numerical methodologies with the potential to improve the efficiency of tropical cyclone LES in the future. The first is a pioneering non-column based implementation of the Kessler warm rain microphysics parametrization, a method which would allow for the use of three-dimensional (3D) adaptive mesh refinement (AMR) in the simulation of moist tropical cyclones. The second is an implementation of Laguerre-Legendre semi-infinite elements for use in the damping layers of atmospheric models, a method which was shown to be capable of improving the efficiency of benchmark atmospheric simulations. Finally, the dissertation presents a study of two-dimensional (2D) AMR applied to simulations of a rapidly intensifying dry tropical cyclone and shows that AMR is able to accurately reproduce the results of simulations using static grids while demonstrating considerable cost savings. 

Abstract. We introduce ClimateMachine, a new open-source atmosphere modeling framework which uses the Julia language and is designed to be scalable on central processing units (CPUs) and graphics processing units (GPUs). ClimateMachine uses a common framework both for coarser-resolution global simulations and for high-resolution, limited-area large-eddy simulations (LESs). Here, we demonstrate the LES configuration of the atmosphere model in canonical benchmark cases and atmospheric flows using a total energy-conserving nodal discontinuous Galerkin (DG) discretization of the governing equations. Resolution dependence, conservation characteristics, and scaling metrics are examined in comparison with existing LES codes. They demonstrate the utility of ClimateMachine as a modeling tool for limited-area LES flow configurations. 

Abstract Numerical weather prediction is pushing the envelope of grid resolution at local and global scales alike. Aiming to model topography with higher precision, a handful of articles introduced unstructured vertical grids and tested them for dry atmospheres. The next step toward effective high‐resolution unstructured grids for atmospheric modeling requires that also microphysics is independent of any vertical columns, in contrast to what is ubiquitous across operational and research models. In this paper, we present a non‐column based continuous and discontinuous spectral element implementation of Kessler's microphysics with warm rain. We test the proposed algorithm against standard three‐dimensional benchmarks for precipitating clouds and show that the results are comparable with those presented in the literature across all of the tested effective resolutions. While presented for both continuous and discontinuous spectral elements in this paper, the method that we propose can be adapted to any numerical method used in other codes, as long as the code can already handle vertically unstructured grids.