Low-diffusion approximate Riemann solvers for Reynolds-stress transport

The paper investigates the use of low-diffusion (contact-discontinuity-resolving) approximate Riemann solvers for the convective part of the Reynolds-averaged Navier–Stokes (rans) equations with Reynolds-stress model (rsm) for turbulence. Different equivalent forms of the 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, demonstrating enhanced accuracy and satisfactory convergence.