由给定前导激波重构楔形体及其波后流场
Reconstruction of a Wedge and Post-Shock Flow from a Prescribed Leading Shock
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中文总结 AI 辅助
本文通过全欧拉Rankine-Hugoniot关系与简化内部模型，结合hodograph变换，提出一种由给定前导激波重构楔形体及其波后流场的充分准则，并保证唯一C^1流场与C^2楔形体的存在，数值实验验证了其收敛性与马赫数依赖性。
中文摘要 AI 辅助
本文从给定的前导激波和均匀超声速来流状态出发，重构楔形体及其波后流场。全欧拉Rankine-Hugoniot关系提供激波数据，而简化内部模型结合了齐次声学特征方程、熵输运和伯努利关系。通过hodograph变换，得到关于物理坐标的线性双曲方程。将激波到楔体的质量界限与hodograph非退化阈值进行比较，可得到一个依赖于数据的充分重构准则。在所述假设下，该准则确保在由给定激波段确定的特征域内，存在唯一的C^1波后流场和C^2楔形体。数值重构检验了经验网格收敛性、马赫数依赖性，以及简化模型与全欧拉逆重构之间的差异。
英文摘要
In this paper, we reconstruct a wedge and its post-shock flow from a prescribed leading shock and a uniform supersonic incoming state. Full Euler Rankine--Hugoniot relations supply the shock data, while a reduced interior model combines homogeneous acoustic characteristic equations, entropy transport, and the Bernoulli relation. A hodograph transformation yields a linear hyperbolic equation for the physical coordinate. Comparing a shock-to-wedge mass bound with a hodograph non-degeneracy threshold gives a sufficient, data-dependent reconstruction criterion. Under the stated assumptions, this criterion ensures a unique \(C^1\) post-shock flow and a \(C^2\) wedge throughout the characteristic domain determined by the prescribed shock segment. Numerical reconstructions examine empirical grid convergence, Mach-number dependence, and discrepancies between the reduced-model and full-Euler inverse reconstructions.
发表机构
- Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·阿列克桑德大学）
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