A quasi-implicit time advancing scheme for unsteady incompressible flow. Part I: Validation

A quasi-implicit fractional-step method is presented for computing unsteady incompressible flow on unstructured grids. A non-staggered grid system is employed rather than a staggered grid system because of the simplicity and ease of extension to three-dimensional analysis. In this study, the momentum interpolation method, developed by Rhie and Chow [C.M. Rhie, W.L. Chow, Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA J. 21 (1983) 1525–1532] and further extended by Zang et al. [Y. Zang, R.L. Street, J.R. Koseff, A non-staggered grid, fractional-step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates, J. Comput. Phys. 114 (1994) 18–33], is applied to problems on unstructured grids to resolve the pressure oscillation problem occurring in a non-staggered grid system. An implicit time advancing scheme is used in order to remove the time step restriction and to reduce the required CPU time for problems with complex geometries. The nonlinear equations resulting from this fully implicit scheme are linearized without deteriorating the overall time accuracy. The system matrices are solved using the CG family method, known with P-BiCGSTAB, for momentum equation and P-CG for pressure Poisson equation. The present numerical method is applied to solve four benchmark problems and the results show good agreement with previous experimental and numerical results.