Contributed Talk
Automatic step size selection for error control on semi-lagrangian schemes of kinetic equations
Gran Sasso Science Institute, L'Aquila, Italy
Abstract
Kinetic equations are well known for their applications in several fields such as gas dynamics, plasma physics, traffic flow, swarming dynamics and socioeconomic modeling. Several numerical methods for solving this kind of equations have been deeply studied in the last decades, (Eulerian solvers, fully lagrangian solvers, semi-lagrangian solvers). However, the issue of step size selection for extimate and control the local error has not been deeply investigated so far. Controlling the error can have important advantages in terms of stability and robustness of the solver. In this talk, I will investigate the implementation of step size control for the Runge-Kutta semi-lagrangian scheme, focusing on the case of BGK equation (Russo, Groppi, Stracquadanio, 2015), which is well known for its application in weakly collisional gas dynamics, and I will discuss the main advantages of the resulting scheme in terms of efficiency and accuracy.