An accurate interpolating scheme for semi - Lagrangianadvection on an unstructured mesh for oceanmodelling

The semi-Lagrangian method is used for advection experiments on an irregular grid. A cosine hill is advected using a speci ed ow eld corresponding to solid body rotation. A major di culty is to nd 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 signi cant even if the interpolation is performed separately on smaller subdomains. However, by taking advantage of the increased exibilty 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.