An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood ...An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood element is introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the algorithm, the numerical simulation on plane Poisseuille flow problem and lid- driven cavity flow problem with different Reynolds numbers is presented. The numerical results indicate that the proposed iterative version can be effectively applied to the simulation of viscous incompressible flows. Moreover, the proposed iterative version has a better overall performance in maximum time step size allowed, under comparable convergence rate, stability and accuracy, than other tested versions in numerical solutions of the plane PoisseuiUe flow with different Reynolds numbers ranging from low to high viscosities.展开更多
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 cu...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.展开更多
该文基于SMAC(simplified marker and cell)方法,发展了一种在任意曲线坐标系中求解不可压黏性层流的全隐数值格式。基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。所有方程离散在MAC交错网格系统中进行。...该文基于SMAC(simplified marker and cell)方法,发展了一种在任意曲线坐标系中求解不可压黏性层流的全隐数值格式。基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。所有方程离散在MAC交错网格系统中进行。根据构造的全隐数值格式自编程序对一可简化成二维层流的后台阶流场进行计算,通过与已有的实验结果和计算结果进行比较,确认目前的计算结果优于比较的计算结果,和实验结果也相当吻合。为进一步验证该数值格式的可靠性,扩展程序对三维后台阶层流进行计算,结果表明,三维计算结果比二维计算结果更加接近实验结果。展开更多
In this work, a new numerical scheme is proposed for thermal/isothermal incompressible viscous flows based on operator splitting. Unique solvability and stability analysis are presented. Some numerical result are give...In this work, a new numerical scheme is proposed for thermal/isothermal incompressible viscous flows based on operator splitting. Unique solvability and stability analysis are presented. Some numerical result are given, which show that the proposed scheme is highly efficient for the thermal/isothermal incompressible viscous flows.展开更多
该文基于SM AC(s im p lified m arker and ce ll)方法,发展了一种在任意曲线坐标系中求解三维粘性不可压湍流R eyno lds时均方程的全隐式数值方法。基本方程是以逆变速度为变量的R eyno lds时均动量方程和椭圆型压力Po isson方程,并采...该文基于SM AC(s im p lified m arker and ce ll)方法,发展了一种在任意曲线坐标系中求解三维粘性不可压湍流R eyno lds时均方程的全隐式数值方法。基本方程是以逆变速度为变量的R eyno lds时均动量方程和椭圆型压力Po isson方程,并采用标准k-ε湍流模型封闭方程组。压力Po isson方程用T schebyscheff SLOR方法交替方向迭代求解。R eyno lds时均动量方程、k方程和ε方程对流项均采用Chakravarthy-O sher TVD格式离散,该格式不但有助于提高数值稳定性,而且能有效消除网格扭曲较大的地方产生的非物理振荡误差。用自编程序对后台阶方腔流场进行了计算,计算结果和实验结果吻合较好。展开更多
基金the National Natural Science Foundation of China (No. 50778111)the Key Project of Fund of Science and Technology Development of Shanghai(No. 07JC14023)the Doctoral Disciplinary Special Research Project of Chinese Ministry of Education(No. 200802480056)
文摘An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood element is introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the algorithm, the numerical simulation on plane Poisseuille flow problem and lid- driven cavity flow problem with different Reynolds numbers is presented. The numerical results indicate that the proposed iterative version can be effectively applied to the simulation of viscous incompressible flows. Moreover, the proposed iterative version has a better overall performance in maximum time step size allowed, under comparable convergence rate, stability and accuracy, than other tested versions in numerical solutions of the plane PoisseuiUe flow with different Reynolds numbers ranging from low to high viscosities.
基金The project was supported by the Natural Science Foundation of Zhejiang Province(196045)the National Natutal Science Foundation of China(19472055).
文摘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.
文摘该文基于SMAC(simplified marker and cell)方法,发展了一种在任意曲线坐标系中求解不可压黏性层流的全隐数值格式。基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。所有方程离散在MAC交错网格系统中进行。根据构造的全隐数值格式自编程序对一可简化成二维层流的后台阶流场进行计算,通过与已有的实验结果和计算结果进行比较,确认目前的计算结果优于比较的计算结果,和实验结果也相当吻合。为进一步验证该数值格式的可靠性,扩展程序对三维后台阶层流进行计算,结果表明,三维计算结果比二维计算结果更加接近实验结果。
基金Acknowledgments. The work of the first author was supported by the grants of the National Natural Science Foundation of China （10971165, 10901122, 11001216, 11026051）.
文摘In this work, a new numerical scheme is proposed for thermal/isothermal incompressible viscous flows based on operator splitting. Unique solvability and stability analysis are presented. Some numerical result are given, which show that the proposed scheme is highly efficient for the thermal/isothermal incompressible viscous flows.
文摘该文基于SM AC(s im p lified m arker and ce ll)方法,发展了一种在任意曲线坐标系中求解三维粘性不可压湍流R eyno lds时均方程的全隐式数值方法。基本方程是以逆变速度为变量的R eyno lds时均动量方程和椭圆型压力Po isson方程,并采用标准k-ε湍流模型封闭方程组。压力Po isson方程用T schebyscheff SLOR方法交替方向迭代求解。R eyno lds时均动量方程、k方程和ε方程对流项均采用Chakravarthy-O sher TVD格式离散,该格式不但有助于提高数值稳定性,而且能有效消除网格扭曲较大的地方产生的非物理振荡误差。用自编程序对后台阶方腔流场进行了计算,计算结果和实验结果吻合较好。
