This is the joint work with Gissell Estrada-Rodriguez and Diane Peurichard.
By formal arguments, the diffusion limit of nonlinear kinetic equations, where both the transport term and the turning operator are density-dependent, leads to volume-exclusion chemotactic (Keller-Segel) equations.
We generalise an asymptotic preserving scheme for such nonlinear kinetic equations based on a micro-macro decomposition. By properly discretizing the nonlinear term implicitly-explicitly in an upwind manner, the scheme produces accurate approximations also in the case of strong chemosensitivity.
The scheme can be proven to be asymptotic preserving and bound preserving, which are essential for practical applications.
Future Work:
- A high-order AP and positive-preserving method for the kinetic model