Numerical Simulations with a Three-Dimensional Spectral Element Model

Highly accurate numerical methods for solving partial differential equations that have been traditionally used in the computational fluid dynamics have yet to be fully exploited for geophysical fluid dynamics applications, such as weather prediction. We will present results obtained with a fully compressible, non-hydrostatic spectral element (SE) model in three dimensions. All of our results are obtained using an eighth order polynomial (p=8), which provides the best compromise between accuracy and computational cost. The number of elements (h), into which the computational domain is decomposed, is varied among experiments to achieve different effective spatial resolutions. Introducing physical parameterizations into an SE model is challenging due to a number of aspects including the varying nodal spacing within each element. We highlight some of these challenges and our approaches to address them. The model is applied in a series of idealized experiments that include physical process parameterizations such as: i) flow over complex terrain with sub-grid scale mixing, and ii) a sea breeze that includes an evolving planetary boundary layer with surface fluxes. We discuss the issues that arise when physical parameterizations are introduced into SE models. Also, scalability results over many computational cores will be addressed. In addition, we will compare the efficiency and accuracy of the results with a finite difference model (FD).