A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids

Abstract

A new second-order time-accurate fractional-step method for solving unsteady incompressible Navier–Stokes equations on hybrid unstructured grids is presented. The nonstaggered grid method, originally developed by Rhie and Chow (1983, AIAA J.21, 1525) for steady flow and further extended by Zang et al. (1994, J. Comput. Phys.114, 18) to unsteady flow on structured grids, is employed in the present study to enforce mass conservation on hybrid unstructured grids. The pressure and Cartesian velocity components are defined at the center of each cell, while the face-normal velocities are defined at the mid-points of the corresponding cell faces. A second-order fully implicit time-advancement scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy. Both the momentum and Poisson equations are integrated with the finite volume method and the flow variables at the cell face are obtained using an interpolation scheme independent of cell shape. The present numerical method is applied to four different benchmark problems and proves to be accurate and efficient.