Reynolds-stress-model-VLES multiblock implicit solver using high-order upwind schemes

Abstract

The purpose of the present paper is to report progress in the development of a flow-solver methodology using second-moment-transport-based continuous turbulence models, which dynamically adapt from RANS to DNS, depending on available numerical spacetime resolution. Space-discretization uses high-order (up to O[ΔxH9]) upwind-biased primitive-variables- MUSCL reconstruction for the convective fluxes, combined with an HLLC approximate Biemann solver. Time-integration uses implicit O[Δt 2] backward-differences, with dual-time-stepping subiterations. The number of subiterations is chosen dynamically, on the basis of an increment-convergence-tolerance criterion. Depending on the ratio of the required physical-time-step on the numerical-stability-time-step, the subiterative procedure can be implicit or explicit. The conservation equations for the resolved-flow-variables and the transport-equations for the apparent stresses (associated with the unresolved scales) are solved on multiblock structured grids, where neighbouring blocks communicate using a phantom-nodes technique, which preserves high-order spatial accuracy. Typical RSM-RANS, DNS, and RSM-PANS results are presented, and compared with measurements.