A well-balanced scheme able to cope with hydrodynamic limits for linear kinetic models

Well-balanced schemes were introduced to numerically enforce consistency with longtime behavior of the underlying continuous PDE. When applied to linear kinetic models, like the Goldstein-Taylor system, this construction generates discretizations which are inconsistent with the hydrodynamic stiff limit (despite it captures diffusive limits quite well). A numerical hybridization, taking advantage of both time-splitting (TS) and well-balanced (WB) approaches is proposed in order to fix this defect: numerical results show that resulting composite schemes improve rendering of macroscopic fluxes while keeping a correct hydrodynamic stiff limit.