Applications of a Three-Dimensional Finite Element Model to Mountain-Valley Flows.

摘要

In this paper we will describe briefly a modified finite element procedure which we have developed to solve the non-hydrostatic planetary boundary layer equations. We have exploited several cost effective procedures such as a one-point quadrature scheme and mass lumping in conjunction with an explicit, modified forward Euler, time integration scheme. This simplified approach enables us to achieve computational efficiencies competitive with standard finite difference models. In addition we employ an iterative technique based on a preconditioned conjugate gradient algorithm for the time-consuming pressure solution portion of the model. In order to realistically model the atmospheric flows of interest we have implemented a ''K-Theory'' (variable eddy diffusivity) model to parameterize the turbulent fluxes within the boundary layer. The K-model proposed by McNider and Pielke is used for application in nocturnal (stable) situations. In this formulation the vertical eddy diffusion coefficients are calculated as a function of the local Richardson number, a measure of the local stability of an air parcel. In daytime (convective) situations, we employ an O'Brien cubic profile to model the vertical variation of the eddy diffusivities. We will present results from simulations in which we employ surface cooling to the approximated surface terrain of Brush Creek to simulate drainage flows down the valley. In particular we will focus attention on comparisons of the model results or the down-valley wind with the observed data. The performance of the proposed variable K turbulence model will be evaluated by comparisons with results from a constant K model and also with observations. 5 refs., 3 figs. (ERA citation 13:049553)