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参照Ｌａｘ－Ｗｅｎｄｒｏｆｆ格式的构造方法，就双曲型方程、抛物型方程和双曲－抛物型方程，构造了一种新的ＩＲＳ（ｉｍｐｌｉｃｉｔｒｅｓｉｄｕａｌｓｍｏｏｔｈｉｎｇ）格式．该ＩＲＳ格式有二阶或三阶时间精度且大大地拓宽了解的稳定区域和ＣＦＬ数．这种新的ＩＲＳ格式有中心加权型和迎风偏向型两种，并用ｖｏｎ－Ｎｅｕｍａｎｎ分析方法分析了格式的稳定范围．讨论了在透平机械中广泛应用的Ｄａｗｅｓ方法的局限性，发现该方法对稳态问题得出的解与时间步长的选取有关，对粘性问题求解时，时间步长受严格限制．最后，结合 ＴＶＤ（ｔｏｔａｌ ｖａｒｉａｔｉｏｎ ｄｉｍｉｎｉｓｈｉｎｇ）格式和四阶Ｒｕｎｇｅ－Ｋｕｔｔａ技术，用 ＩＲＳ格式和 Ｄａｗｅｓ方法对二维反射激波场进行了数值模拟，数值结果支持本文的分析结论．
With reference to the construction method of Lax-Wendroff format, a new IRS (implicitresidualsmoothing) format is constructed for hyperbolic equations, parabolic equations and hyperbolic-parabolic equations. The IRS format has second- or third-order time accuracy and greatly broadens the understanding of stable regions and CFL numbers. The new IRS format has two kinds of center-weighted and windward-oriented type, and the stability range of the format is analyzed by von-Neumann analysis method. The limitations of the Dawes method widely used in turbomachinery are discussed. It is found that the solution to the steady-state problem is related to the choice of the time step, and the time step is strictly limited when the viscous problem is solved. Finally, combining the TVD (total variation diminishing) scheme and the fourth-order Runge-Kutta technique, two-dimensional reflection shock fields are simulated by the IRS and Dawes methods. The numerical results support the conclusion of this paper.