Dan Whitt, Columbia University

Numerical Approximation of Coordinate Transformations

Abstract: When numerically solving PDEs using a spectral element method, one often has to transform the coordinate system from a physical domain to a computational domain. When this is the case, there are a set of metric identities which must hold. This amounts to requiring that constants remain constant after coordinate transformations and time stepping. When one discretizes the PDEs, a new set of metric identities must be satisfied. We test numerical coordinate transformations which satisfy the new metric identities against current analytical transformations. We also make use of 3D-Cartesian coordinates in our physical domain instead of latitude/longitude to avoid continuity problems at the pole and the prime meridian.

Presentation slides (ppt)