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In this paper, we establish the first rigorous mathematical global result on the validation of the hypersonic similarity, which is also called the Mach-number independence principle, for the two dimensional steady potential flow. The…

Analysis of PDEs · Mathematics 2019-11-07 Jie Kuang , Wei Xiang , Yongqian Zhang

For the three-dimensional steady non-isentropic compressible Euler system with friction, we show existence of a class of symmetric subsonic, supersonic and transonic-shock solutions in a straight duct with constant square-section. Such…

Analysis of PDEs · Mathematics 2018-11-02 Hairong Yuan , Qin Zhao

How to determine accurately and efficiently the aerodynamic forces of the aircraft in high-speed flow is one of great challenges in modern aerodynamics. In this Letter we propose a new similarity law for steady transonic-supersonic flow…

Fluid Dynamics · Physics 2022-08-25 Luoqin Liu

Compressible flow varies from ideal-gas behavior at high pressures where molecular interactions become important. Density is described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and…

Fluid Dynamics · Physics 2020-03-11 William A. Sirignano

In this paper, we study the existence of a global transonic shock generated by hypersonic potential flow over a large curved convex wedge. Modeling 2-dimensional steady potential flow leads to a free boundary value problem of quasilinear…

Analysis of PDEs · Mathematics 2025-08-06 Dian Hu

We investigate the steady inviscid compressible self-similar flows which depends only on the polar angle in spherical coordinates. It is shown that besides the purely supersonic and subsonic self-similar flows, there exists purely sonic…

Analysis of PDEs · Mathematics 2025-01-20 Shangkun Weng , Hongwei Yuan

We perform particle-resolved simulations of subsonic and transonic flows past random arrays of spherical particles. The Reynolds number is held at $Re{\approx}300$ to ensure the flow remains in the continuum regime. At low volume fractions,…

Fluid Dynamics · Physics 2022-08-23 Mehdi Khalloufi , Jesse Capecelatro

We are concerned with inverse problems for supersonic potential flows past infinite axisymmetric Lipschitz cones. The supersonic flows under consideration are governed by the steady isentropic Euler equations for axisymmetric potential…

Analysis of PDEs · Mathematics 2023-10-30 Gui-Qiang G. Chen , Yun Pu , Yongqian Zhang

By a combination of asymptotic ODE estimates and numerical Evans function calculations, we establish stability of viscous shock solutions of the isentropic compressible Navier--Stokes equations with $\gamma$-law pressure (i) in the limit as…

Analysis of PDEs · Mathematics 2017-06-09 Jeffrey Humpherys , Olivier Laffite , Kevin Zumbrun

Hypersonic waveriders are special shapes with leading edges coincident with the body's shock wave, yielding high lift-to-drag ratios. The waverider geometry results from streamline tracing using the solutions of a basic flow field such as…

Fluid Dynamics · Physics 2024-03-20 Agnivo Ghosh , Srisha M V Rao

This study aims to shed light on hypersonic attachment-line instabilities with large sweep Mach numbers. Highly swept flows over a cold cylinder that give rise to large sweep Mach numbers are studied. High fidelity base flows are obtained…

Fluid Dynamics · Physics 2021-07-01 Youcheng Xi , Jie Ren , Song Fu

We construct with full rigorous mathematical proof a family of approximate solutions to the Cauchy problem for the standard system of two fluid flows with energy equations and we pass to the limit by weak compactness to obtain Radon…

Analysis of PDEs · Mathematics 2019-07-09 M. Colombeau

We investigate the relaxation problem for the one-dimensional pressureless Euler--Poisson equations with the initial density being a finite Radon measure. The entropy solution of this linearly degenerate hyperbolic system converges to the…

Analysis of PDEs · Mathematics 2025-07-22 GuiRong Tang

We analyse a bi-fluid isentropic compressible Navier-Stokes system with barotropic pressure laws in a two-phase framework with equal pressure and single velocity. We focus on the rigorous analysis of the low Mach number limit under…

Analysis of PDEs · Mathematics 2026-04-06 Cassandre Lebot

A compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our…

Analysis of PDEs · Mathematics 2016-06-22 Gui-Qiang G. Chen , Feimin Huang , Tian-Yi Wang , Wei Xiang

In this short note we present an instability result for transonic flows with respect to perturbations of the Mach number at infinity. More specifically we show that a perturbation of a transonic solution in the context of a Cauchy problem…

Analysis of PDEs · Mathematics 2021-09-29 Yannis Angelopoulos

The probability density function (PDF) of the gas density in subsonic and supersonic, isothermal, driven turbulence is analyzed with a systematic set of hydrodynamical grid simulations with resolutions up to 1024^3 cells. We performed a…

Solar and Stellar Astrophysics · Physics 2014-11-27 Lukas Konstandin , Philipp Girichidis , Christoph Federrath , Ralf S. Klessen

The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic…

Analysis of PDEs · Mathematics 2009-04-24 Xianpeng Hu , Dehua Wang

Analytical/quasi-analytical solutions are proposed for a steady, compressible, two-phase flow in mechanical equilibrium in a rectilinear duct subjected to heating followed by cooling. The flow is driven by the pressure ratio between a…

Fluid Dynamics · Physics 2024-04-17 Solène Schropff , Fabien Petitpas , Eric Daniel

We prove the incompressible limit of non-isentropic inviscid elastodynamic equations with general initial data in 3D half-space. The deformation tensor is assumed to satisfy the neo-Hookean linear elasticity and degenerates in the normal…

Analysis of PDEs · Mathematics 2024-12-16 Jiawei Wang , Junyan Zhang