Application of a Multigrid Method to a Mass-Consistent Diagnostic Wind Model

Abstract

A multigrid numerical method has been applied to a three-dimensional, high-resolution diagnostic model for flow over complex terrain using a mass-consistent approach. The theoretical background for the model is based on a variational analysis using mass conservation as a constraint. The model was designed for diagnostic wind simulation at the microscale in complex terrain and in urban areas. The numerical implementation takes advantage of a multigrid method that greatly improves the computation speed. Three preliminary test cases for the model?s numerical efficiency and its accuracy are given. The model results are compared with an analytical solution for flow over a hemisphere. Flow over a bell-shaped hill is computed to demonstrate that the numerical method is applicable in the case of parameterized lee vortices. A simulation of the mean wind field in an urban domain has also been carried out and compared with observational data. The comparison indicated that the multigrid method takes only 3%?5% of the time that is required by the traditional Gauss?Seidel method.