Asymptotic Preserving and Multiscale Methods for Kinetic and Hyperbolic Problems

Asymptotic preserving simulations of kinetic systems for chemotaxis

Alina Chertock

North Carolina State University


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.