SIX-DIMENSIONAL ADAPTIVE SIMULATION OF THE VLASOV EQUATIONS USING A HIERARCHICAL BASIS

Erwan Deriaz (1) , Sébastien Peirani (2)

1 IJL - Institut Jean Lamour
2 IAP - Institut d'Astrophysique de Paris

We present an original adaptive scheme using a dynamically refined grid for the simulation of the six-dimensional Vlasov-Poisson equations. The distribution function is represented in a hierarchical basis retaining only the most significant coefficients. This allows considerable savings in terms of computational time and memory usage. The proposed scheme massively relies on the computational Adaptive Mesh Refinement framework. For the moment we embed it into a simple finite difference method. Numerical experiments are presented for the d-dimensional Vlasov-Poisson equations in the full 2d-dimensional phase space for d = 1, 2 and 3. The six-dimensional case is compared to a Gadget N-body simulation.

Mots clés: hierarchical basis; wavelet; multiresolution analysis; finite differences; phase-space simulations; Vlasov--Poisson equations; astrophysics; adaptive mesh refinement

Domaines: Analyse numérique [math.NA]

Erwan Deriaz, Sébastien Peirani. SIX-DIMENSIONAL ADAPTIVE SIMULATION OF THE VLASOV EQUATIONS USING A HIERARCHICAL BASIS. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2018, 16 (2), pp.583-614. ⟨10.1137/16M1108649⟩. ⟨hal-01419750v2⟩