An accurate interpolating scheme for semi-Lagrangian advection on an unstructured mesh for ocean modelling

Abstract

The semi-Lagrangian method is used for advection experiments on an irregular grid. A cosine hill is advected using a specified flow field corresponding to solid body rotation. A major difficulty is to find an interpolator which is at least fourth order accurate on an unstructured mesh. Such accuracy is needed for the treatment of Rossby waves in ocean models. We develop such a method using a dual kriging interpolating scheme. The results are better than fourth order accurate, as shown by comparison with bicubic spline interpolation on a structured grid. Such accuracy is maintained for an unstructured triangular grid. The dissipation and dispersion of the cosine hill remain small, even after many rotation periods. The increase in computational cost is significant even if the interpolation is performed separately on smaller subdomains. However, by taking advantage of the increased flexibility of unstructured meshes and accuracy of the kriging approach, it is possible to achieve the same accuracy at a reasonable computational cost compared to traditional methods.