A New Approximate LU Factorization Scheme for the Reynolds-Averaged Navier-Stokes Equations

A new approximate LU factorization scheme is developed to solve the steady-state Reynolds-averaged NavierStokes (NS) equations. Central differencing is used for both implicit and explicit operators, and special care is taken to obtain well-conditioned factors on the implicit side. The scheme is then analyzed and optimized according to a simple linear analysis. It is unconditionally stable for the model hyperbolic equation in both two and three dimensions. However, the requirement for well-conditioned factors has essentially limited the effective time step that the scheme can achieve. Supersonic and transonic 3-D flows past a hemisphere cylinder are computed to demonstrate the convergence characterstics of the scheme. A good convergence rate is achieved in the inviscid case. Finally, an explicit eigenvector annihilation procedure is employed successfully to remove the stiffness caused by the fine grid spacing for viscous flows.

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