Asymptotic Preserving and Multiscale Methods for Kinetic and Hyperbolic Problems

Asymptotic preserving simulations of kinetic systems for chemotaxis

Alina Chertock

North Carolina State University
[SLIDES]

We consider numerical approximations of the kinetic equations describing a collective behavior of bacteria and their interaction with both nutrients and chemoattractant. We introduce a non-dimensional small parameter (epsilon=the ratio of the mean free paths corresponding to isotropic and chemotactic reorientation) and by choosing a diffusion scaling we obtain a transport equation in nondimensional form depending on this parameter. In [Chalub et al. (2004)] the conditions have been derived under which the drift-diffusion limit of this Fokker-Planck system yields the Keller-Segel model. With respect to this result our aim is to investigate asymptotic preserving schemes for the corresponding kinetic chemotaxis equations.