Abstract Numerical simulation of aerodynamic problems using an algorithm, which identifies shock regions and refines the mesh there using an adaptive mesh refinement method, is performed. The static mesh adaptation method is based on cell partitioning by adding new nodes to cell faces. The method of identification of the shock regions using a pressure and density gradient criterion and its verification are presented. The use and applications of the developed algorithm are illustrated, and supersonic and hypersonic flows with strong shock waves are calculated. The results computed explore the shock-wave structure of the flow, which develops near the nose cone section of a body and determines its aerodynamic performance. The aerodynamic performance of bodies with different nose cone designs, including a body with a spike and a pointed cone with an opposing gas jet injected from the nose section, are evaluated based on the proposed method. The method of static mesh adaptation provides a visually sharper picture of the flow around the body and reduces the numerical error of drag coefficient calculations in comparison with wind tunnel measurements. The results computed on meshes of similar resolution constructed with the adaptation method and automatic mesh generator are compared. The results computed on the adaptive mesh are similar to those computed on the mesh generated automatically, but the adaptive mesh has a smaller number of cells.

中文翻译：

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基于自适应网格细化方法的气动问题数值模拟

摘要 使用一种算法对空气动力学问题进行数值模拟，该算法识别冲击区域并使用自适应网格细化方法细化那里的网格。静态网格自适应方法基于通过向单元面添加新节点的单元划分。介绍了使用压力和密度梯度准则识别冲击区的方法及其验证。说明了所开发算法的使用和应用，并计算了具有强冲击波的超音速和高超音速流动。计算结果探索了流动的冲击波结构，该结构在身体的鼻锥部分附近发展并决定了其空气动力学性能。不同鼻锥设计的车身空气动力学性能，包括一个带有尖刺的物体和一个带有从鼻子部分注入的相反气体射流的尖锥体，基于所提出的方法进行评估。与风洞测量相比，静态网格自适应方法提供了视觉上更清晰的身体周围流动图像，并减少了阻力系数计算的数值误差。比较了使用自适应方法和自动网格生成器构建的相似分辨率网格的计算结果。在自适应网格上计算的结果与在自动生成的网格上计算的结果相似，但自适应网格的单元数较少。与风洞测量相比，静态网格自适应方法提供了视觉上更清晰的身体周围流动图像，并减少了阻力系数计算的数值误差。比较了使用自适应方法和自动网格生成器构建的相似分辨率网格的计算结果。在自适应网格上计算的结果与在自动生成的网格上计算的结果相似，但自适应网格的单元数较少。与风洞测量相比，静态网格自适应方法提供了视觉上更清晰的身体周围流动图像，并减少了阻力系数计算的数值误差。比较了使用自适应方法和自动网格生成器构建的相似分辨率网格的计算结果。在自适应网格上计算的结果与在自动生成的网格上计算的结果相似，但自适应网格的单元数较少。