A study of parameter-free shock capturing upwind schemes on low speeds' issues

Nowadays, the upwind schemes are in a rapid development to capture shock accurately. However, these upwind schemes' properties at low speeds, such as their reconstruction scheme dependencies, grid dependencies, and Mach number dependencies, are concerned by few people. In this paper, a systematic study on their low speeds' issues is conducted. Through a series of tests, we can find that most parameter-free upwind schemes, widely used in practice today, are not applicable to low speeds' simulations. In contrast, SLAU and SLAU2 can give reliable results. Also, the upwind scheme's influence on the accuracy is stronger than the reconstruction scheme's influence at low speeds.