改进的基于特征线的N-S方程算子分裂有限元法

Improved characteristic-based operator-splitting finite element for Navier-Stokes equations

基于特征线的Navier-Stokes(N-S)方程算子分裂有限元法(CBOS有限元法)的核心是在每一个时间层上,采用算子分裂法将N-S方程的对流项和扩散项分开求解;对流项的求解过程借鉴了简单显式特征线时间离散,显式求解。该文在原CBOS有限元法基础上推导了一种更加精确的对流项显式离散方法。通过自编程序对方腔流进行数值模拟,表明该算法具有更高的计算精度。低雷诺数下圆柱绕流计算所得的阻力系数、升力系数、斯特劳哈数等与已有数据较为接近,表明该文中算法能较准确地模拟圆柱绕流的流场特性;最后,文中分析了Re=200时圆柱绕流在一个周期内所受升力变化与对应流场中压力和流线演化的关系。

The pivotal ideas of characteristic-based operator-splitting（CBOS） finite element method for Navier-Stokes equations are that the equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm in each time step.The convective part can be discretized using the simple explicit characteristic temporal discretization and solved explicitly.On the basis of CBOS finite element method,an exact explicit discrete method is developed.The improved method has higher calculation accuracy through numerical simulation of lid-driven cavity flow.Furthermore,the method is used to simulate the incompressible viscous flow around cylinder with low Reynolds number.The numerical results agree well with other numerical results,which proves that it can exactly simulate the characteristics of flow around cylinder.Finally,the relationship between a cycle of lift coefficient and the corresponding development of pressure and streamline is analyzed at Re=200.