熵变量欧拉方程组跨超声速流SUPG有限元数值解

通过变量代换将拟线性守恒变量欧拉方程组转换为具有对称性的熵变量欧拉方程组，对该方程组构造SUPG的弱解式，其中权函数摄动项中包含流向算子和间断捕获算子。对翼型的跨超声速流动算例表明，本法具有较好的稳定性和能有效地抑制激波两侧振荡。应用带预处理的GMRES迭代法求解非对称方程组能显著地提高收敛速度。

SUPG Finite Element Numerical Solution in Entropy Variables for Transonic and Supersonic Flows

The Euler equations of quasi-linear form in conservation variables can be transformed into the Euler equations of symmetric form in entropy variables by introducing the change of variables. The SUPG weak statement of the above set of equations has been constituted. The perturbation terms of Weighting function include the streamlines operator and the discontinuity-capturing operator.A number of numericalIv com-puted examples on the airfoils at transonic and supersonic flows demon-strate that the present method shows better stability and suppresses effec-tively the oscillation on both sides of the shock. Employing the precon-ditioned GMRES iterative algorithm to resolve the nonsvmmetric set of equations can remarkably enhance the convergent rate.