IMPLICIT SOLUTION METHOD FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONS INCLUDING 2-LAYER K-TAU TURBULENCE MODEL

The two-dimensional incompressible Navier-Stokes equations including a low-Reynolds-number two-layer k-tau turbulence model are solved by an implicit time-stepping routine using the method of artificial compres sibility. The two-layer model uses a transport equation for the turbul ent kinetic energy k and a new algebraic relationship for the turbulen t time scale tau near the wall but reverts to the two-equation k-tau t urbulence model in the bulk of the flow away from the wall. The algebr aic relationship for the turbulent time scale tau and the eddy-viscosi ty damping function f(mu) are validated by direct numerical simulation data and asymptotic analysis of near-wall turbulence. A fifth-order u pwind-biased differencing scheme is used to discretize the convective and pressure terms and second-order central differences are employed f or other spatial derivatives. The nonlinear equations are solved using the preconditioned generalized minimal residual technique in conjunct ion with numerical linearization. A LD(-1)U factorization of the appro ximate Jacobian matrix is used as preconditioning matrix. The iterativ e scheme has good vectorization properties and runs at about 160 Mflop s on one processor of a Gray Y-MP. The results for turbulent channel h ows at low Reynolds numbers are in good agreement with direct numerica l simulation data even in the viscous sublayer. Compared with experime ntal data, the simulation of the turbulent flow over a backward-facing step in a parallel and a diverging channel shows a better agreement f or the reattachment length than comparable two-equation models.