Atmospheric Modeling with High-Order Finite-Volume Methods.

Abstract

This thesis demonstrates the versatility of high-order finite-volume methods for atmospheric general circulation models. In many research areas, these numerical methods have been shown to be robust and accurate, and further have many properties which make them desirable for modeling atmospheric dynamics. However, there have been few attempts to implement high-order methods in atmospheric models, and none that use finite-volume methods. High-order methods are desirable for future model development due to their superior wave propagation properties and necessity when using adaptive mesh refinement.

The thesis describes in detail a hierarchy of atmospheric models that utilize high-order finite-volume methods. The hierarchy includes a 2D shallow-water model, both 2D and 3D non-hydrostatic models and a 3D non-hydrostatic dynamical core in spherical geometry. These models span atmospheric motions that range from the microscale, mesoscale to the global-scale regime while essentially leaving the underlying numerical scheme unchanged. A cubed-sphere computational grid has been chosen for the global models, due to its relative uniformity as compared with the traditional regular latitude-longitude grid. First, the thesis documents the development of a finite-volume-based remapping scheme for accurately converting data between cubed-sphere and latitude-longitude meshes. An analysis of several finite-volume-type methods in 1D for advection is then presented, with some emphasis on models with grid adaptation. Furthermore, the thesis describes the formulation of the model hierarchy that represents a gradual increase in complexity and thereby serves as a testbed. The 2D (x-y) shallow-water model on the sphere evaluates explicit time-stepping algorithms and demonstrates how to accurately handle the panel boundaries of the cubed-sphere mesh. The 2D-slice (x-z) and 3D non-hydrostatic finite-volume models in Cartesian geometry introduce an implicit-explicit time-splitting technique needed to properly handle the small grid spacings and high-speed waves in the vertical direction. Finally, a novel 3D non-hydrostatic high-order finite-volume dynamical core in cubed-sphere geometry is presented. The thesis demonstrates that high-order finite-volume methods are a viable and promising option for future atmospheric models, and an important stepping stone for next-generation atmospheric model development.