二维不可压N-S方程二次四边形单元有限元解

粘性不可压流体问题是众多工程中重要的力学问题.数值求解Navier-Stokes方程会遇到两大困难:非线性和不可压性.针对二维不可压Navier-Stokes方程的特点,建立了以流函数为求解变量的四阶微分控制方程,有效地避免了处理涡量边界的难题.采用8节点二次四边形单元,单元基函数为2次非线性高阶函数,建立了求解二维不可压N-S方程的有限元方程,并自主开发了二次四边形单元有限元程序.数值实验结果验证了该方法的精确性和可靠性.因此,该方法在计算流体力学中有较好的应用前景.

Finite Element Method with Quadratic Quadrilateral Unit forSolving Two Dimensional Incompressible N-S Equation

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems.Because of high non linear and incompressibility for Navier-Stokes equation,it is very difficult to solve Navier-Stokes equation by numerical method.According to its characters of Navier-Stokes equation,quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly.The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition.Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.Based on it,the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed.Lastly,numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics.