A review of strongly coupled algorithms for viscous flow problems

Numerical solution of the fluid dynamic equations requires appropriate discretization, quasi-linearization and choice of algorithm. For the latter, approximate factorization procedures put forth by Beam and Warming have played a significant role in the successful completion of this task. The present authors have demonstrated that another element, strong coupling of the discrete equations with the discrete form of the boundary conditions, can play an equally important role. In the present study, the significance of this coupling on the effectiveness of several approximate factorization techniques for the solution of the Navier–Stokes equations is reviewed. It it shown that, even with strong coupling, no single iterative solution algorithm is optimal for the entire spectrum of the flow problems considered.