Two-dimensional simulations of flow over idealized topography using a spectral element model

Highly accurate numerical methods for solving partial differential equations that have been traditionally used in the computational fluid dynamics are being considered in the geophysical fluid dynamics as well. We are presenting results obtained with a fully compressible, non-hydrostatic spectral element (Continuous Galerkin) model. Its accuracy is determined by the polynomial order (p) of basis functions and number of elements (h) into which the original domain is subdivided.

The model is used in a series of two dimensional experiments of flow over idealized topography. The computational domain is divided into equally sized elements (h in horizontal direction) and within each element the solution is expressed as a sum of basis functions (p^th order Lagrange polynomials), using unevenly spaced nodal (Legendre-Gauss-Lobatto) points. By varying number of elements (h) from 6 to 120 and polynomial orders (p) from 4 to 10, the hp parameter space was mapped out, resulting in 91 sets of parameters.

For each set of parameters, idealized simulations (dry, inviscid, linear, hydrostatic, no rotation) were performed and assessed by comparing the solution of u, w and momentum flux to the analytic solution. Results obtained by a finite difference model were also compared for assessment of computational efficiency. The method, experimental setup, error statistics, speed of convergence to the steady–state solution and spectral (hp) convergence will be presented.