Hypersonic Similarity for the Two Dimensional Steady Potential Flow with Large Data

• DOI: 10.48550/arxiv.1911.02159
• Publication Date: 2019-01-01
• Authors: Jie Kuang; Wei Xiang; Yongqian Zhang
• Keywords: Similarity (geometry); Similarity solution

In this paper, we establish the first rigorous mathematical global result on validation of hypersonic similarity, which is also called Mach-number independence principle, for two dimensional steady potential flow. The similarity equivalent to Van Dyke's theory, that if parameter $K$ fixed, shock solution structures (after scaling) are consistent, when Mach number flow sufficiently large. One difficulty after scaling, solutions usually large data since perturbation not small related sonic speed. order make it, employ modified Glimm scheme construct approximate with and find fine structure elementary wave curves obtain existence entropy data, fixed incoming $M_{\infty}$. Finally, further show a $K$, $M_{\infty}\rightarrow\infty$, obtained above approach corresponding initial-boundary value problem small-disturbance equations. Therefore, theory verified rigorously.