Split-type implicit scheme using flux splitting and dual-time step for Euler equations

Abstract

There are some shortcomings of the traditional implicit schemes such as complex forms and large amount of computations. Using the idea of operator splitting combining with implicit discrete schemes—flux vector splitting and dual-time step scheme—a simpler split-type implicit difference scheme for Euler equations was developed. The validity and reliability of the new implicit scheme were verified by performing numerical experiments on some typical problems in aerodynamics,and the properties of the new scheme were discussed in detail at the same time. The new scheme has common advantages of good stability and few constraints on time step just like other implicit schemes. In addition,the new scheme has the following advantages: it has simple formulas; it is easy for programming; it needs smaller amount of computations by avoiding solving systems of equations and doing inverse matrix operation compared with conventional implicit schemes in single time step; it has faster convergence rate compared with LU-SGS scheme.