Comparison of Traditional and Novel Discretization Methods for Advection Models in Numerical Weather Prediction

Numerical Weather Prediction has been dominated by low order finite difference methodology over many years. The advent of high performance computers and the development of high order methods over the last two decades point to a need to investigate the use of more advanced numerical techniques in this field. Domain decomposable high order methods such as spectral element and discontinuous Galerkin, while generally more expensive (except perhaps in the context of high performance computing), exhibit faster convergence to high accuracy Solutions and can locally resolve highly nonlinear phenomena. This paper presents comparisons of CPU time, number of degrees of freedom and overall behavior Of Solutions for finite difference, spectral difference and discontinuous Galerkin methods on two model advection problems. In particular, spectral differencing is investigated as an alternative to spectral-based methods which exhibit stringent explicit time step requirements.