The Generalized Integral Transform Technique (G.I.T.T.) is extended to handle the incompressible NavierStokes equations for two-dimensional steady laminar¯ow in cylindrical geometries. Hybrid numerical-analytical solutions with controlled accuracy are obtained, as a result of an appropriate choice of the associated eigenfunction expansion basis, extracted from the diffusion operator of the stream function-only formulation for this class of problems. The approach is illustrated for developing laminar¯ow within an annular channel and numerical results are obtained to demonstrate the excellent convergence characteristics of this hybrid method. Critical comparisons against the boundary layer formulation are provided, and a set of benchmark results is produced, for different values of Reynolds number and aspect ratio.
The Generalized Integral Transform Technique (GITT) is utilized in the hybrid numerical-analytical solution of the Reynolds averaged Navier-Stokes equations, for developing turbulent¯ow inside a parallel-plates channel. An algebraic turbulence model is employed in modelling the turbulent diffusivity. The automatic global error control feature inherent to this approach, permits the determination of fully converged reference results for the validation of purely numerical methods. Therefore, numerical results for different values of Reynolds number are obtained, both for illustrating the convergence characteristics of the integral transform approach, and for critical comparisons with previously reported results through different models and numerical schemes.
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