  The paper investigates the use of low-diffusion
(contact-discontinuity-resolving [Liou M.S.: {\em J. Comp. Phys.} {\bf 160}
(2000) 623--648]) approximate Riemann solvers for the convective part of the
Reynolds-averaged Navier-Stokes (\tsn{RANS}) equations with Reynolds-stress
model (\tsn{RSM}) closure. Different equivalent forms of the \tsn{RSM-RANS}
system are discussed and classification of the complex terms introduced by
advanced turbulence closures is attempted. Computational examples are
presented, which indicate that the use of contact-discontinuity-resolving
convective numerical fluxes, along with a passive-scalar approach for the
Reynolds-stresses, may lead to unphysical oscillations of the solution. To
determine the source of these instabilities, theoretical analysis of the
Riemann problem for a simplified Reynolds-stress transport model-system, which
incorporates the divergence of the Reynolds-stress tensor in the convective
part of the mean-flow equations, and includes only those nonconservative
products which are computable (do not require modelling), was undertaken,
highlighting the differences in wave-structure compared to the passive-scalar
case. A hybrid solution, allowing the combination of any low-diffusion
approximate Riemann solver with the complex tensorial representations used in
advanced models, is proposed, combining low-diffusion fluxes for the mean-flow
equations with a more dissipative massflux for Reynolds-stress-transport.
Several computational examples are presented to assess the performance of this
approach.
