This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of characteristics. The approach is simple to implement, generates entropic solutions, and avoids solving Riemann problems. A diffusion control parameter is introduced to increase the accuracy of the scheme. Numerical examples are presented for the Euler equation for an ideal gas. The results demonstrate the method's ability to capture contact discontinuity and shock wave profiles with high accuracy and low cost as well as its robustness.

翻译：本文提出了一种基于有限体积方法的高精度守恒型双曲系统求解格式。该创新方法利用特征线法构造控制体界面处的中间状态，具有实现简便、生成熵解、无需求解黎曼问题等优势。通过引入扩散控制参数提高了格式的求解精度。针对理想气体欧拉方程的数值算例表明，该方法能以较低计算成本高精度捕捉接触间断和激波剖面，同时展现出良好的鲁棒性。