新的解跨音速Euler方程的隐式杂交方法

 本文提出一个新的杂交格式,它由Jameson-Turkel LU分解法和Harten TVD（total variation diminishing）格式的修正数值通量耦合而成。LU分解用于Euler方程隐式部分的离散化而Harten的数值通量控制所谓的稳态解残差。精心构造LU算子,可使矩阵算子L和U很容易逐点推进求逆;以Harten的数值通量计算杂交格式右边的通量,这样做在a=1/2的条件下,可保证收敛的稳态解具有二阶精度并能高分辨率地捕获激波。数值实验表明,本文格式对于稳态计算是有生命力的并能保证较高的激波分辨率。

A NEW IMPLICIT HYBRID SCHEMES FOR THE EULER EQUATION OF TRANSONIC FLOW

A new implicit hybrid scheme, by coupling the Jameson and Turkel's LU decompositions with modified viscous terms in Harten's TVD(total variation diminishing) formulation is presented. The LU decomposition is applied to discretize the implicit part of the Euler equations and the Harten's viscous terms to handle the usually called residual of steady-state solutions. With carefully constructed LU factors the inversion of such a scheme can be very easy and efficient since only one explicit point by point sweep is necessary for each LU factor.With the Marten's modified flux function to calculate the right hand side operators of the hybrid scheme, such treatment can guarantee the second order accuracy of the converged steady-state solutions under the condition of a =1/2 and high resolution in capturingshock waves. Numerical experiments show that the scheme is quite robust and can generate good shock resoution for steady-state computations.