Efficient Numerical Methods for Unstructured Triangular Meshes in Ocean Modeling Applications

Triangular locally refined meshes offer advantages in ocean modeling, since they are capable of representing complex basin geometries much more accurately than orthogonal rectangular meshes. This advantage is crucial for applications, in which accurate coastal dynamics is the focus of investigation – like tsunami inundation. On the other hand, accurate and efficient numerical operators are much easier to develop and implement on orthogonal structured meshes. Therefore, accurate numerical schemes need to be designed for triangular meshes, capable of preserving the conservation properties of the underlying continuous equations, and robust against grid distortion. Furthermore, in order to gain efficiency, some structure needs to be imposed on the triangular meshes. By this, efficient computational algorithms can be designed, which might be able to compete - in terms of efficiency - with current structured mesh schemes.
(joern.behrens@zmaw.de)