The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for this purpose and are typically based on Riemann solvers, which are strongly dependent on the underlying eigen-structure of the governing equations. Objective of the present work is to develop simple algorithms which are not dependent on the eigen-structure and yet can tackle easily the hyperbolic parts. Central schemes with smart diffusion mechanisms are apt for this purpose. For fixing the numerical diffusion, the basic ideas of satisfying the Rankine-Hugoniot (RH) conditions along with generalized Riemann invariants are proposed. Two such interesting algorithms are presented, which capture grid-aligned steady contact discontinuities exactly and yet have sufficient numerical diffusion to avoid numerical shock instabilities. Both the algorithms presented are robust in avoiding shock instabilities, apart from being accurate in capturing contact discontinuities, do not need wave speed corrections and are independent of eigen-struture of the underlying hyperbolic parts of the systems.

可压缩流体流动的控制方程中的非线性对流项本质上是双曲线的，对于建模和数值模拟来说是非常重要的。在过去的几十年中，为此目的开发了许多数值方法，并且通常基于黎曼求解器，后者强烈依赖于控制方程的基本特征结构。当前工作的目标是开发不依赖于特征结构但可以轻松处理双曲线部分的简单算法。具有智能扩散机制的中央方案适用于这一目的。为了解决数值扩散问题，提出了满足Rankine-Hugoniot (RH)条件以及广义黎曼不变量的基本思想。提出了两个这样有趣的算法，准确捕捉网格对齐的稳定接触不连续性，并且具有足够的数值扩散以避免数值冲击不稳定性。所提出的两种算法在避免冲击不稳定性方面都很稳健，除了在捕捉接触不连续方面准确之外，不需要波速校正，并且独立于系统底层双曲线部分的本征结构。