Efficiency Gains in Coastal Ocean Modeling Through High-order Solution Algorithms

Over the past 20-30 years, the accuracy improvements in numerical coastal ocean models have been realized through greatly increasing mesh resolution in order to properly resolve the physical processes in the nearshore and reduce the numerical dissipation inherent in the solution method. This increase in resolution has resulted in computationally costly simulations that have been made feasible alongside advances in parallel computing technology. However, the accuracy of the underlying numerical methods of these models has largely remained at second order. This means that although these models may produce well-validated results, the potential to improve their efficiency is limited. High-order methods offer a means to lower the computational expense by way of their higher formal error convergence rate as a function of mesh resolution and greater efficiency on a cost-per-accuracy basis. This allows high-order algorithms to be used with coarser domain resolution to maintain the same level of accuracy as today's state-of-the-art models at reduced cost. Despite these advantages, the implementation of high-order algorithms poses challenges that expose instabilities and/or prevent the resulting solutions from being truly high-order, negating the expected efficiency gains. In the context of coastal ocean models, this means describing the domain geometry, bathymetry, and parameter fields with greater fidelity on coarse resolution meshes. This talk will give an overview of the implementation of iso- and super-parametric elements and the generation of high-order bathymetry and parameter fields with a moving least squares technique to create a fully-high order model domain. Through a simulation of the Galveston Bay area, it will be shown that the combination of a high-order algorithm and high-order domain description can provide solutions of similar accuracy to a highly resolved, low-order model with reduced computational expense.