High-Order Algorithms for 3D Plasma Simulations on Unstructured and Hybrid Meshes

摘要

The work completed under this project builds on our previous work sponsored by AFOSR on developing a universal spectra basis for formulating algorithms for high-order accurate solutions of arbitrary nonlinear systems of PDEs in complex-geometry domains. To this end, several classes of classical numerical methods (e.g. finite elements and finite volumes) as well as modern methods (e.g. spectral and spectral elements) are simply subcases of the developed new numerical methodology. On of the unique features of the new methods is that its accuracy is insensitive to the mesh quality, which allows simulation in moving and very distorted domains (without re-gridding) at extremely high-efficiencies, not possible with any other method.