By introducing hybrid technique into high-order CPR (correction procedure via reconstruction) scheme, a novel hybrid WCNS-CPR scheme is developed for efficient supersonic simulations. Firstly, a shock detector based on nonlinear weights is used to identify grid cells with high gradients or discontinuities throughout the whole flow field. Then, WCNS (weighted compact nonlinear scheme) is adopted to capture shocks in these areas, while the smooth area is calculated by CPR. A strategy to treat the interfaces of the two schemes is developed, which maintains high-order accuracy. Convergent order of accuracy and shock-capturing ability are tested in several numerical experiments; the results of which show that this hybrid scheme achieves expected high-order accuracy and high resolution, is robust in shock capturing, and has less computational cost compared to the WCNS.

中文翻译：

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守恒律冲击捕获的高阶混合WCNS-CPR方案

通过将混合技术引入高阶CPR（通过重建的校正过程）方案，开发了一种新型的WCNS-CPR混合方案，用于高效的超声模拟。首先，基于非线性权重的冲击检测器用于识别在整个流场中具有高梯度或不连续性的网格单元。然后，采用WCNS（加权紧凑非线性方案）捕获这些区域的震动，而平滑区域通过CPR计算。开发了一种处理这两种方案的接口的策略，该策略保持了高阶精度。在几个数值实验中，测试了精度和捕捉能力的收敛顺序。结果表明，该混合方案可实现预期的高阶精度和高分辨率，并且具有强大的震荡捕获能力，