A new full discrete stabilized viscosity method for transient Navier-Stokes equations
A new full discrete stabilized viscosity method for transient Navier-Stokes equations
复制标题
DOI：
10.1007/s10483-009-0704-z
复制
发表时间：
2009-07
影响因子：
--
通讯作者：
Yan-mei Qin;M. Feng;Tianxiao Zhou
中科院分区：
文献类型：
--
作者：
Yan-mei Qin;M. Feng;Tianxiao Zhou
基于压力投影和外推梯形法则，提出了一种新的求解高雷诺数（小粘性系数）瞬态Navier-Stokes方程的全离散稳定粘性方法。在空间上采用连续等阶有限元，在时间上采用简化的Crank-Nicolson格式，对瞬态Navier-Stokes方程进行全离散。新的稳定化方法是稳定的，并且具有许多吸引人的性质。首先，由于增加了压力投影项，使得系统对于离散连续速度空间和压力空间的等阶组合是稳定的。第二，在粘性系数中加入人工粘性参数作为稳定因子，使系统具有抗扩散性。最后，该方法只需要在每个时间步的线性系统的解决方案。证明了该方法的稳定性和收敛性。误差估计结果表明，该方法具有二阶精度，估计中的常数与粘性系数无关。数值结果表明了该方法的优越性。
A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number (small viscosity coefficient) is proposed based on the pressure projection and the extrapolated trapezoidal rule. The transient Navier-Stokes equations are fully discretized by the continuous equal-order finite elements in space and the reduced Crank-Nicolson scheme in time. The new stabilized method is stable and has many attractive properties. First, the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pressure projection term. Second, the artifical viscosity parameter is added to the viscosity coefficient as a stability factor, so the system is antidiffusive. Finally, the method requires only the solution to a linear system at every time step. Stability and convergence of the method is proved. The error estimation results show that the method has a second-order accuracy, and the constant in the estimation is independent of the viscosity coefficient. The numerical results are given, which demonstrate the advantages of the method presented.