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

Well-balanced schemes were introduced to numerically enforce consistency with long-time 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.