中文摘要：

将一种基于多维修正的Osher通量运用于高阶加权紧致非线性格式（WCNS）中,该修正通量主要在垂直于激波面的界面上增加耗散,能够改善Osher通量的激波捕捉稳定性,同时对边界层和接触间断的分辨率影响非常小。对修正的Osher通量在高阶WCNS中的特性进行研究,通过数值模拟测试了基于Osher通量的WCNS的激波稳定性、热流预测精度、边界层模拟能力、激波边界层干扰模拟能力,并与Steger-Warming通量和Roe通量进行了对比。结果表明修正后的Osher通量比Harten修正的Roe通量具有更好的激波捕捉鲁棒性,而边界层、驻点热流值和激波边界层干扰的模拟则明显优于Steger-Warming通量。上述结果说明了基于修正的Osher通量的高阶WCNS具有较好的激波捕捉特性、热流预测精度和边界层计算能力。

英文摘要：

Osher flux with a multi-dimensional entropy fix is applied for high order weighted compact nonlinear scheme （WC- NS）. The entropy fix technique is used to mainly improve the dissipation on the interfaces perpendicular to the shock wave, and can thus improve shock wave stability and may not influence contact resolution. The properties of the Osher flux in high order WCNS schemes are studied. Numerical investigations are made to test properties of shock wave stability, accuracy of viscous heating computation, and boundary layer and shock boundary layer interaction calculation abilities. Comparisons with Steger-Warming flux and Roe flux are also made. Numerical results show that the Osher flux with entropy fix is more robust than Roe flux with Harten fix in shock capturing, and is better in viscous heating computation than Steger-Warming flux. These results illustrate that high order WCNS based on Osher flux with entropy fix is robust in caputuring shock waves, can get accurate heat flow prediction and has good simulation of the boundary layer.