Resumen
We derive and study well-balanced schemes for quasi-monotone discrete kinetic models. By means of a rigorous localization procedure, we reformulate the collision terms as nonconservative products and solve the resulting Riemann problem, whose solution is self-similar. The construction of an asymptotic preserving (AP) Godunov scheme is straightforward, and various compactness properties are established within different scalings. Finally, some computational results are supplied to show that this approach is realizable and efficient on concrete 2 × 2 models.