超声速和高超声速粘性绕流QPNS方程的GLS有限元解

从完全非定常Ｎ－Ｓ方程（ＦＮＳ）中略去流向粘性导数导出拟抛物Ｎ－Ｓ方程（ＱＰＮＳ），ＱＰＮＳ技术结合经典抛物推进和拟时松弛，拟时松弛能有效地抑制解的发散。本文导出的熵变量形式ＱＰＮＳ方程具有对称性和自动满足热力第二定律，这将提高解的稳定性，伽辽金／最小二乘法（ＧＬＳ）被用来构造ＱＰＮＳ的弱解式。对于钝前缘物体，ＱＰＮＳ在前缘区并不适用，本文代之以用ＦＮＳ求解该区，由离散解得到的非对称线性方程组，对

Solution of QPNS Equations for Supersonic and Hypersonic Viscous Past Flows Using GLS FEM

The quasi-parabolic Navier-Stokes(QPNS) equations are derived from the fully unsteady Navier-Stokes equations(FNS) by neglecting streamwise viscous derivatives. The QPNS technique is to combine the classical parabolic marching approach with a quasi-time relaxation which can suppress all divergent solutions efficiently. The QPNS equations in entropy variables derived in the present paper have the symmetrization and satisfy the second law of thermodynamics automatically that can improve the stability of the solution.The Galerkin/Least-square FEM is applied to construct the weak formulation of QPNS equations. For bodies with the blunt nose, the QPNS equations are not applicable to the nose region. Instead,the FNS equations are employed to solve such region. The exit plane of nose region is used as an initial data plane to start a QPNS calculation. The nonsymmetric and linear equations from the discrete solution are solved by using block tridiagonal systems for the QPNS equations and by GMRES algorithm for the FNS equations. Numerical examples are the supersonic/hypersonic flows past the flat plate with semi-cylindried nose at incidence. The numerical results compared with the available experimental data and the numerical solution are encouraging.