SNuBic Seminar talk by Andres Galindo-Olarte
Oden Institute for Computational Engineering and Sciences at University of Texas Austin
A Tour on Kinetic Equations
Abstract:
In this talk, we will present numerical analysis and experiments for various numerical schemes applied to kinetic equations. These include the Discontinuous Galerkin (DG) method, spectral methods, and other innovative approaches.
Specifically, we will cover:
- Post-processing of DG solutions for the Vlasov-Maxwell equations to enhance accuracy through SIAC filtering.
- Numerical analysis of a hybrid method for Radiation Transport that balances computational efficiency and accuracy.
- An unconditionally conservative local DG method for the Fokker-Planck-Landau equation to ensure preservation of physical invariants through a structure-preserving scheme.
- A hybrid DG/Low-Rank approximation for the BGK equation aimed at reducing computational costs while maintaining solution fidelity.
Our findings highlight the importance of rigorous numerical analysis and tailored methods to either conserve physical quantities, reduce computational costs, or effectively address the multi-scale phenomena inherent in kinetic simulations.
