Simulations

Numerical simulation of the Vlasov-Poisson BGK model in the diffusive scaling using an Asymptotic Preserving hybrid scheme. The method automatically adapts in position the state of the cells (kinetic or fluid) and the numerical solver used. This method allows for significant reduction of the computational time.

Numerical simulation of a non-linear kinetic reaction model. The model consists in studying the phase-space densities of two reactants in a solution. One can show that the solution to this model converges exponentially fast in time towards a steady state that is constant in position.

Numerical simulation of a kinetic relaxation model in a large deviation scaling. We work with the Hopf–Cole transform of the kinetic distribution, approximated using an Asymptotic Preserving scheme. In the limit, the model becomes a non-local Hamilton–Jacobi equation. A striking feature here is that the small-parameter limit and the long-time behaviour do not commute:  for any fixed positive parameter the system relaxes to a constant profile, while the limit model keeps a memory of the initial data.