A Godunov-type scheme and a relaxation scheme are presented to approximate the solutions of the convective subsystem arising from the transport equations of a class of second-order turbulence-moment models in the framework of incompressible flows. An analytical representation is proposed for the case of the occurrence of a non-turbulent region. Numerical tests of the two schemes and a comparison with a Rusanov scheme complete the paper.
Bouchiba et al. (Wed,) studied this question.