A computational method for the Favre-Reynolds-averaged three-dimensional compressible Navier-Stokes equations using near-wall Reynolds-stress closure is described. The near-wall Reynolds-stress closure uses the Launder-Shima formulation for the Reynolds stresses and the Jones-Launder-Sharma modified dissipation (e*) equation. The mean-flow and turbulence-transport equations are discretized using a finite volume method based on MUSCL Van Leer flux-vector-splitting with Van Albada limiters. The mean-flow and turbulence equations are integrated in time using a fully coupled approximately factored implicit backward Euler method. The resulting scheme is robust and achieves optimal convergence with local-time-step Courant-Friedrichs-Lewy = 50. The turbulence closure is validated by comparison with classic flat-plate boundary-layer data. Results are presented for the three-dimensional Delery transonic channel test case and compared with k-e computations. An analysis of the limitations of the closure is attempted, and possible improvements are suggested.
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Gerolymos et al. (1997) studied this question.
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