In this study we couple a family of AUSM-flux splitting schemes with the CENO high-order scheme and evaluate the overall performance of the developed in-house solver in terms of modeling the flow physics accurately for a wide range of benchmark problems. The solver uses reconstructed conservative variables. The problems include inviscid and viscous flows that cover low subsonic through transonic and hypersonic regimes. We test the order of accuracy of the implemented CENO scheme by interpolating a smooth spherical cosine function and then calculating the L-norms. The obtained results confirm the consistency between the spatial accuracy and the order of reconstruction up to 5th order. We are able to reach 4th order of accuracy in time by using a Runge-Kutta scheme and thereby we obtain a perfect match with the WENO results available in the literature for the unsteady problem of interaction of a moving vortex with a stationary normal shock. In order to reduce the computational cost of the developed solver and to be able to model more challenging problems, we utilize the advantageous adaptive mesh refinement that allows us to resolve the discontinuities near shocks and slip lines. Our adaptive mesh refinement algorithm is based on a smoothness indicator factor, and allows us to reach the same level of accuracy as the WENO schemes do for the inviscid double Mach reflection problem by using considerably less amount of cells.

在这项研究中，我们将一系列 AUSM 通量分裂方案与 CENO 高阶方案结合起来，并评估开发的内部求解器在为各种基准问题准确建模流动物理方面的整体性能。求解器使用重建的保守变量。这些问题包括通过跨音速和高超音速机制覆盖低亚音速的无粘性和粘性流动。我们通过内插平滑的球面余弦函数然后计算 L 范数来测试实现的 CENO 方案的精度顺序。获得的结果证实了空间精度和重建顺序之间的一致性，最高可达 5 阶。通过使用 Runge-Kutta 方案，我们能够在时间上达到 4 阶精度，因此我们获得了与文献中可用的 WENO 结果的完美匹配，用于解决移动涡流与静止法向激波相互作用的不稳定问题。为了降低开发的求解器的计算成本并能够模拟更具挑战性的问题，我们利用了有利的自适应网格细化，使我们能够解决冲击和滑移线附近的不连续性。我们的自适应网格细化算法基于平滑度指标因子，使我们能够通过使用相当少的单元来达到与 WENO 方案对无粘性双马赫反射问题相同的精度水平。为了降低开发的求解器的计算成本并能够模拟更具挑战性的问题，我们利用了有利的自适应网格细化，使我们能够解决冲击和滑移线附近的不连续性。我们的自适应网格细化算法基于平滑度指标因子，使我们能够通过使用相当少的单元来达到与 WENO 方案对无粘性双马赫反射问题相同的精度水平。为了降低开发的求解器的计算成本并能够模拟更具挑战性的问题，我们利用了有利的自适应网格细化，使我们能够解决冲击和滑移线附近的不连续性。我们的自适应网格细化算法基于平滑度指标因子，使我们能够通过使用相当少的单元来达到与 WENO 方案对无粘性双马赫反射问题相同的精度水平。