Abstract
A (2+2)-dimensional kinetic equation, directly inspired by the run-and-tumble modeling
of chemotaxis dynamics is studied so as to derive a both ''2D well-balanced'' and
''asymptotic-preserving'' numerical approximation. To this end, exact stationary regimes
are expressed by means of Laplace transforms of Fourier-Bessel solutions of associated
elliptic equations. This yields a scattering S-matrix which permits to formulate a timemarching
scheme in the form of a convex combination in kinetic scaling. Then, in the
diffusive scaling, an IMEX-type discretization follows, for which the ''2D well-balanced
property'' still holds, while the consistency with the asymptotic drift-diffusion equation is
checked. Numerical benchmarks, involving ''nonlocal gradients'' (or finite sampling
radius), carried out in both scalings, assess theoretical findings. Nonlocal gradients appear
to inhibit blowup phenomena.
Anno
2021
Autori IAC
Tipo pubblicazione
Altri Autori
Gabriella Bretti; Laurent Gosse
Rivista
SN Partial Differential Equations and Applications