摘要
This paper presents a higher order difference scheme for the computation of the incompressible viscous flows. The discretization of the two-dimensional incompressible viscous Navier-Stokes equations, in generalized curvilinear coordinates and tensor formulation, is based on a non-staggered grid. The momentum equations are integrated in time using the four-stage explicit Runge-Kutta algorithm [1] and discretized in space using the fourth-order accurate compact scheme [2]. The pressure-Poisson equation is discretized using the nine-point compact scheme. In order to satisfy the continuity constraint and ensure the smoothness of pressure field, an optimum procedure to derive a discrete pressure equation is proposed [9][3] . The method is applied to calculate the driven cavity flow on a stretched grid with the Reynolds numbers from 100 to 10000. The numerical results are in very good agreement with the results obtained by Ghia et al [7] and include the periodic solutions for high Reynolds numbers.
This paper presents a higher order difference scheme for the computation of the incompressible viscous flows. The discretization of the two-dimensional incompressible viscous Navier-Stokes equations, in generalized curvilinear coordinates and tensor formulation, is based on a non-staggered grid. The momentum equations are integrated in time using the four-stage explicit Runge-Kutta algorithm [1] and discretized in space using the fourth-order accurate compact scheme [2]. The pressure-Poisson equation is discretized using the nine-point compact scheme. In order to satisfy the continuity constraint and ensure the smoothness of pressure field, an optimum procedure to derive a discrete pressure equation is proposed [9][3] . The method is applied to calculate the driven cavity flow on a stretched grid with the Reynolds numbers from 100 to 10000. The numerical results are in very good agreement with the results obtained by Ghia et al [7] and include the periodic solutions for high Reynolds numbers.
基金
The project was supported by the Natural Science Foundation of Zhejiang Province(196045)
the National Natutal Science Foundation of China(19472055).
