SEMINAR SERIES and COLLOQUIA

Discontinuous spectral element methods are a relatively new class of schemes emerging in numerical weather prediction. These methods discretize the computational domain into smaller sub-domains in which local spectral approximations are made. The solution in each sub-domain is nearly independent of neighboring solutions except for the computation of a numerical flux at sub-domain interfaces. These methods provide spectral accuracy and are the seemingly ideal discretization for massively parallel computing architectures.

The mathematical formulation of two such schemes, discontinuous Galerkin and spectral difference, will be described. A series of one- and two-dimensional test cases are evaluated using these methods and compared with finite differences, with respect to both accuracy and computation time. It is found that in general the discontinuous spectral element methods provide better accuracy for the same amount of computation time. The spectral difference method is built into the framework of a two-dimensional, non-hydrostatic model and used for scalar advection. This model and its finite difference counterpart will be compared for a density current simulation.

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