关键词: 跨音速流, Euler方程, 数值计算

Abstract:

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.

Key words: transonic flow, Euler's equation, numerical calcula-tion