三维N-S方程计算隐式有限体积法

利用NND有限差分格式，发展了一种新的完全隐式的有限体积数值方法，以求解与时间相关的N－S方程．对通过单元体界面的无粘流和粘性流通量均作隐式处理．对绕流钝锥体和不同攻角的气动辅助实验飞行器的高超声速粘性流和化学反应流获得了定常数值解．对流加热率和流场电子密度的计算值与实验数据进行了比较，符合较好，证实了本方法的精确性．

IMPLICIT FINITE VOLUME METHOD FOR THREE-DIMENSIONALNAVIER-STOKES COMPUTATION

In this study, a new fully-implicit finite-volume numerical algorithm is developed tosolve the time-dependent Navier-Stokes equations using NND finite difference scheme. Both inviscid and viscous fluxes across cell boundaries are treated implicitly. The present work emphasizesthe finite-volume approximation of the integral form of the conservation laws. The integral approach enhances both stability and accuracy of the algorithm. Nonequilibrium reacting hypersonicionizing air viscous flows over the reentry vehicles are investigated and numerically simulated bythe Navier-Stokes equations with the chemical source terms. The global continuity equation is replaced by the conservation equations of individual species. For the high temperature ionized air there are seven primary constituents: N2, O2, NO, NO , N, O, and e-. Chemical kinetics are described by 7 species and 6 possible reactions between these species. The governing equations inconservation form including multicomponent, finite-rate chemical reactions are solved to demonstrate the ability of the technique. All the computations are performed using shock-capturingmethods. The non-catalytic surface boundary condition is treated for the chemical species. The steady state numerical solutions are obtained for hypersonic viscous and Chemically reacting flows over the blunted cones and three-dimensional blunt-body at different angles of attack. We have successfully avoided the stiffness problem by treating the source term implicitly. Good comparisons with experimental data and other numerical results for pressure distributions, heat transfer distributions, and electron densities in the flow field have been demonstrated for three-dimensional blunt-body flows. Good agreements are obtained and verify the accuracy of the present method.