Numerical investigation of Landau damping in dynamical Lorentz gases

Thierry Goudon (1) , Léo Vivion (1)

1 COFFEE - COmplex Flows For Energy and Environment

We investigate numerically the behavior of a particle, or a set of particles, which exchange momentum and energy with the environment, described as a transverse vibrational field. The large time behavior is characterized, in some specific circumstances, by means of effective friction force and Landau damping. In order to discuss these issues on numerical grounds, we set up a dedicated numerical method. The scheme couples a Finite Element Method for the wave equation, with an appropriate transparent boundary condition that preserves the dispersive effects driving the asymptotic behavior of the system, and a symplectic scheme or a Semi-Lagrangian method for the evolution of the particles. The time discretisation is constructed to capture accurately the energy exchanges. The numerical simulations shed new light on the theoretical results and bring out clearly the role of the parameters of the models.

Mots clés: Vlasov–like equations; Interacting particle; Landau dampi; Inelastic Lorentz gas; Finite elements and semi-Lagrangian schemes

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Thierry Goudon, Léo Vivion. Numerical investigation of Landau damping in dynamical Lorentz gases. Physica D: Nonlinear Phenomena, 2019. ⟨hal-02418404⟩