The FORCE-type centred schemes are simple and efficient and do not explicitly require the wave propagation information of the system to calculate the numerical flux. However, their poor resolution for contact discontinuities seriously affects their applications. In the present work, a simple FORCE-type centred scheme accurate for contact discontinuities is proposed and applied to calculations of compressible Euler flows. The missing contact wave of the original FORCE centred scheme is restored with an algebraic method and the resolution for contact discontinuities is further improved by using the boundary variation diminishing (BVD) algorithm to minimize the density jump in the numerical diffusion term of the original FORCE centred scheme. Numerical results of several one- and two-dimensional benchmark test problems fully demonstrate that the proposed centred scheme is capable of capturing contact discontinuities more sharply than the complete-wave HLLC upwind scheme. In addition, another advantage of the proposed centred scheme is that it is free from the carbuncle phenomenon which afflicts many contact-capturing upwind schemes (e.g. Roe and HLLC) in calculations of multidimensional flow problems involving strong shock waves.

FORCE 型居中方案简单有效，并且不明确要求系统的波传播信息来计算数值通量。然而，它们对接触不连续性的较差分辨率严重影响了它们的应用。在目前的工作中，提出了一种对接触不连续性准确的简单 FORCE 型中心方案，并将其应用于可压缩欧拉流的计算。使用代数方法恢复原始 FORCE 中心方案的缺失接触波，并通过使用边界变化递减 (BVD) 算法使原始 FORCE 中心方案的数值扩散项中的密度跳跃最小化，进一步提高了接触不连续性的分辨率方案。几个一维和二维基准测试问题的数值结果充分表明，所提出的居中方案能够比全波 HLLC 逆风方案更清晰地捕捉接触不连续性。此外，所提出的居中方案的另一个优点是，在涉及强冲击波的多维流动问题的计算中，它没有影响许多接触捕获逆风方案（例如 Roe 和 HLLC）的痈现象。