NUMERICAL HIGH-FIELD LIMITS IN TWO-STREAM KINETIC MODELS AND 1D AGGREGATION EQUATIONS

Laurent Gosse (1) , Nicolas Vauchelet (2)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"
2 LJLL - Laboratoire Jacques-Louis Lions

Numerical resolution of two-stream kinetic models in strong aggregative setting is considered. To illustrate our approach, we consider an 1D kinetic model for chemotaxis in hydro-dynamic scaling and the high field limit of the Vlasov-Poisson-Fokker-Planck system. A difficulty is that, in this aggregative setting, weak solutions of the limiting model blow up in finite time, therefore the scheme should be able to handle Dirac measures. It is overcome thanks to a careful discretization of the macroscopic velocity resulting of Vol'pert calculus: accordingly, a new well-balanced (WB) and asymptotic preserving (AP) numerical scheme is provided. Numerical simulations confirm a good behavior of solutions.

Mots clés: Asymptotic-Preserving and Well-Balanced scheme; Chemotaxis dynamics; Duality measure solutions; high-field limit; two-stream kinetic model; Vlasov-Poisson-Fokker-Planck system

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

Laurent Gosse, Nicolas Vauchelet. NUMERICAL HIGH-FIELD LIMITS IN TWO-STREAM KINETIC MODELS AND 1D AGGREGATION EQUATIONS. SIAM Journal on Scientific Computing, 2016. ⟨hal-01233245⟩