GPU Programming in Fortran : Differential Geometry and the Metric Identities

In this livestream, Joe will go over the details for handling coordinate system transformations from physical to computational space. In the process, we will derive the metric identities to motivate the use of the curl invariant form for calculating the contravariant basis vectors in 3-D. Additionally, we'll show an example problem where failing to satisfy the metric identities numerically can lead to spurious solutions that arise solely due to mesh curvature. From here, we'll cover a strategy to resolve this problem in SELF by implementing the curl invariant form of the metric terms in the SELF_Geometry class and revisit the example problem to demonstrate resolution of the issue.

Reference Materials
Links to notes and accompanying materials can be requested at https://opencollective.com/higher-ord...

You can freely download SELF source code online at https://github.com/fluidnumerics/self

Kopriva, D.A. "Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes". J Sci Comput 26, 301 (2006). https://doi.org/10.1007/s10915-005-90...