Numerical High-Field Limits in Two-Stream Kinetic Models and 1D Aggregation Equations
Numerical resolution of two-stream kinetic models in a strong aggregative setting is considered. To illustrate our approach, we consider a one-dimensional kinetic model for chemotaxis in hydrodynamic 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, and therefore the scheme should be able to handle Dirac measures.