Effect of a Simplified Staggered Grid System for Incompressible Flow Computations and Numerical Calculation of Free Surface Flow Problems in Generalized Coordinates

Abstract

Recently, finite-difference schemes for solving the incompressible Navier-Stokes equations involving various kinds of boundary conditions have focused on improving their accuracy, stability and efficiency. A computer program for solving two-dimensional, time-dependent, incompressible viscous flows using the simplified staggered grid in generalized coordinates named SGGQ2D has been developed by using a new formulation better than the former one called GGQ2D with the regular grid. The 2D momentum equations of Navier-Stokes equations for the J^<-1>u artd J^<-1>v velocity components and the Poisson equation for the pressure field are solved by applying a semi-implicit type time-marching scheme. The spurious errors and the numerical instabilities can be suppressed by employing this simplified staggered grid system and the QUICK upwind control volume scheme in generalized coordinates. Some numerical results of a 2D free surface flow that has a obstacle in the upper region of a channel are shown to demonstrate the reliability and robustness of the present scheme. We also suggest the same computation in the regular grid system (see a GGQ2D code), which has more computational time and less conservation of fluid volume, because it causes spurious oscillation of pressure values when it is applied to complex flow fields.