CAJ | 학술논문

基于Hermite多项式的C1型单元构造复杂，限制了最小二乘有限元法的应用。引入高阶光滑的非均匀有理B样条作为基函数简化C1型单元构造，提出求解黏性不可压流动Navier?Stokes方程的最小二乘等几何方法。用Newton法或Picard法对Navier?Stokes方程线性化，用线性化偏微分方程的余量定义最小二乘泛函，导出最小二乘变分方程，用NURBS构造高阶光滑的有限维空间来近似速度场和压力场。计算表明：本文方法计算的二维顶盖驱动流数值解能准确描述流动状况，计算的二维通道内圆柱绕流全局质量损失由最小二乘有限元法的6％降为0?018％，该方法可用于Navier?Stokes方程的求解，并且具有较好的质量守恒性。
기우Hermite다항식적C1형단원구조복잡，한제료최소이승유한원법적응용。인입고계광활적비균균유리B양조작위기함수간화C1형단원구조，제출구해점성불가압류동Navier?Stokes방정적최소이승등궤하방법。용Newton법혹Picard법대Navier?Stokes방정선성화，용선성화편미분방정적여량정의최소이승범함，도출최소이승변분방정，용NURBS구조고계광활적유한유공간래근사속도장화압력장。계산표명：본문방법계산적이유정개구동류수치해능준학묘술류동상황，계산적이유통도내원주요류전국질량손실유최소이승유한원법적6％강위0?018％，해방법가용우Navier?Stokes방정적구해，병차구유교호적질량수항성。
With high order smooth non?uniform rational B?splines ( NURBS) as basis function to simplify C1 element construction, least squares isogeometric analysis is proposed for viscous incompressible Navier?Stokes equations. Governing equations are linearized by Picard or Newton method. Variational equation is derived from least squares functional defined by residuals of linearized equations. High order smooth finite dimensional spaces for velocity and pressure approximation are constructed by NURBS. Two benchmark flow problems were solved. Accurate numerical results were obtained for 2?dimensional lid driven flows. Global mass loss in flow past a cylinder in a channel decreased from 6% in classical least squares finite element method to 0?018%. It shows that the method is applicable to Navier?Stokes equations. It is better in mass conservation than least squares finite element method.