An adaptive multilevel method for boundary layer meteorology

Abstract

This thesis presents a new adaptive multilevel numerical model for incompressible flows and applies such a model for the first time to the simulation of atmospheric boundary layers capped by shallow cumulus and stratocumulus clouds. One needs to simulate a large domain, while locally having enough resolution to resolve the turbulent transports of mass, momentum, heat, and moisture in and around the clouds. Multilevel methods represent the flow on grids of varying resolution and are able to localize the high resolution and computational costs. In an adaptive multilevel method, the optimal regions of refinement are automatically determined and may evolve with time. The composite domain of an adaptive multilevel method is a dynamic balance between the need to resolve the global flow and regions of special interest.In this work, a new forward-in-time multidimensional advection algorithm for incompressible flow with superior stability and accuracy is developed, analyzed and extended to a multilevel flow solver. By using object-oriented numerics and an efficient clustering algorithm, an adaptive numerical model was developed and used to analyze the transport properties of an isolated cumulus cloud. Examples of other forms of boundary layer convection that also benefit from adaptive multilevel modelling are presented for the first time.