We introduce a new variational time discretization for the system of isentropic Euler equations. In each timestep the internal energy is reduced as much as possible, subject to a constraint imposed by a new cost functional that measures the deviation of particles from their characteristic paths. This scheme can also be used for numerical simulations, and I will present some results.
This is joint work with Wilfrid Gangbo and Jon Wilkening.
Back to Workshop I: Aspects of Optimal Transport in Geometry and Calculus of Variations