Abstract: The QPNS equations in the entropy variable are derived from the FNS equations by neglecting streamwise viscous derivatives. The discrete solution always satisfies the entropy production inequality. The QPNS equations are solved with a spacemarching method. The step back strategy is used to provide the data of the initial plane. The Galerkin/least squares finite element method is employed to formulate the weak solution of QPNS equations. The nonsymmetric linear equation systems are solved by GMRES algorithm. The nodal block diagonal preconditioning technique is used to accelerate the convergence rate efficiently. The present method markedly reduces the amount of computer storage and run time. It shows a good stability as well. Numerical examples are the supersonic flows past the parabolic body and tangent ogive body. The results include the pressure, viscous stress, heat flux on the body surface, and the density, temperature in the flow field of windward and leeward.

Key words: GLS finite element method, QPNS equations, rotation body