CAJ | 학술논문

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.
점성불가압류체문제시음다공정중중요적역학문제.수치구해Navier-Stokes방정회우도량대곤난：비선성화불가압성.침대이유불가압Navier-Stokes방정적특점,건립료이류함수위구해변량적사계미분공제방정,유효지피면료처리와량변계적난제.채용8절점이차사변형단원,단원기함수위2차비선성고계함수,건립료구해이유불가압N-S방정적유한원방정,병자주개발료이차사변형단원유한원정서.수치실험결과험증료해방법적정학성화가고성.인차,해방법재계산류체역학중유교호적응용전경.
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.