Hypersonic Similarity for Steady Compressible Full Euler Flows Over Two-Dimensional Lipschitz Wedges

• DOI: 10.48550/arxiv.2304.12925
• Publication Date: 2023-01-01
• Authors: Gui‐Qiang Chen; Jie Kuang; Wei Xiang; Yongqian Zhang
• Keywords: Compressible flow

We establish the optimal convergence rate to hypersonic similarity law, which is also called Mach number independence principle, for steady compressible full Euler flows over two-dimensional slender Lipschitz wedges. The problem can be formulated as comparison of entropy solutions in $BV\cap L^{1}$ between two initial-boundary value problems equations with parameter $\tau>0$ and small-disturbance curved characteristic boundaries. $L^1$--convergence estimate these rate, justifies Van Dyke's theory rigorously flows. This first mathematical result on boundary conditions. To achieve this, we employ special structures systems global existence $L^1$--stability under smallness assumptions total variation both initial data tangential slope wedge boundary. Based properties approximate scaled $\tau$, a uniform Lipschtiz continuous map respect obtained. Next, compare given by Riemann solvers taking perturbations into account case case. Then, fixed parameter, tends infinity, desired rate. Finally, show optimality investigating solution.