Algorithm Development for Vertical Lagrangian Coordinate Based Non-Hydrostatic and Hydrostatic Models.

Abstract

This thesis demonstrates a new non-staggered-grid finite-volume method for dynamical cores in atmospheric general circulation models. Finite volume methods have been proved to be robust and accurate in many research areas. These numerical methods have many properties, which make them desirable for modeling atmospheric dynamics. However, many non-staggered-grid finite-volume methods are numerically expensive because they implement Riemann solvers. To bypass the requirement of using a Riemann solver, current finite volume dynamical cores in the General Circulation Models use less stable staggered grids. We developed a low-cost Riemann solver to implement with the non-staggered-grid schemes, which matches the numerical efficiency of the current staggered-grid schemes. It is much easier to develop a scheme with a high-order of accuracy and which has better performance when using adaptive mesh refinement (AMR) using a non-staggered grid finite volume scheme.

Adaptive mesh refinement is a method that allows one to adaptively capture the features of small-scale motions of particular dynamical interest. However, non-uniform grids are required in adaptive mesh refinement techniques. The varying resolution can cause artificial reflections of waves due to incompatible mechanisms at fine-grid and coarse-grid interfaces. We tested our models using the full set of the conservative Euler equations with non-uniform horizontal grids, in both hydrostatic and non-hydrostatic formulations. Our algorithm for the interface is fully two-way interactive. There is almost no reflection observed in our results and due to the high-order accurate interface, the waves are not damped when passing the interfaces.

Since the vertical distribution of pressure in the atmosphere is a non-polynomial monotonic function, the polynomial based 3D AMR might create pressure gradients at the interface of two grids, even if the atmosphere is initialized statically as a steady state. We introduced an alternative way to find the pressure at any vertical altitude within a control volume using an iterative method. We have shown that in the isentropic atmosphere, the theoretical value of the pressure at any altitude can be determined using this method. Using this method in the vertical volume refinement can prevent creating pressure gradients at the interface between two grids.