High-order space and time accuracy for finite volume schemes

Following some reminders of Florian's talk, we will introduce higher-order space and time discretizations for finite volume schemes, in order to approximate solutions to a conservation law with source terms. Then, we present the space discretization, based on a relevant polynomial reconstruction of the approximate solution as well as a suitable integration of the equations. Afterwards, we propose a time discretization that uses a specific class of Runge-Kutta methods, the SSPRK methods. Finally, some numerical experiments involving the shallow-water equations are performed to highlight the properties of the high-order accuracy.