Converging/Diverging Self-Similar Shock Waves: From Collapse to Reflection

Juhi Jang; Jiaqi Liu; Matthew Schrecker

doi:10.1137/24M1653240

Converging/Diverging Self-Similar Shock Waves: From Collapse to Reflection

Juhi Jang, Jiaqi Liu, Matthew Schrecker

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (SciVal)

77 Downloads (Pure)

Abstract

We solve the continuation problem for the nonisentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar Güderley imploding shock solutions for a perfect gas with adiabatic exponent γ ∊ (1, 3] admit a self-similar extension consisting of two regions of smooth flow separated by an outgoing spherically symmetric shock wave of finite strength. In addition, for γ ∊ (1, ⁵ ₃ ], we show that there is a unique choice of shock wave that gives rise to a globally defined self-similar flow with physical state at the spatial origin.

Original language	English
Pages (from-to)	190-232
Number of pages	43
Journal	Siam Journal on Mathematical Analysis
Volume	57
Issue number	1
Early online date	6 Jan 2025
DOIs	https://doi.org/10.1137/24M1653240
Publication status	Published - 28 Feb 2025

Funding

The first and second authors are supported in part by the NSF grants DMS-2009458 and DMS-2306910. The third author is supported by the EPSRC Post-doctoral Research Fellowship EP/W001888/1

Funders	Funder number
Not added	DMS-2009458, DMS-2306910
Engineering and Physical Sciences Research Council	EP/W001888/1

Keywords

compressible fluid flow
nonisentropic Euler system
radial symmetry
shock wave
similarity solutions

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1137/24M1653240

reflected shock SIMA revised (accepted author manuscript)
Copyright © 2025 Society for Industrial and Applied Mathematics. The final publication is available at SIAM Journal on Mathematical Analysis via https://doi.org/10.1137/24M1653240
Accepted author manuscript, 676 KBLicence: CC BY

Cite this

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title = "Converging/Diverging Self-Similar Shock Waves: From Collapse to Reflection",

abstract = "We solve the continuation problem for the nonisentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar G{\"u}derley imploding shock solutions for a perfect gas with adiabatic exponent γ ∊ (1, 3] admit a self-similar extension consisting of two regions of smooth flow separated by an outgoing spherically symmetric shock wave of finite strength. In addition, for γ ∊ (1, 5 3 ], we show that there is a unique choice of shock wave that gives rise to a globally defined self-similar flow with physical state at the spatial origin.",

keywords = "compressible fluid flow, nonisentropic Euler system, radial symmetry, shock wave, similarity solutions",

author = "Juhi Jang and Jiaqi Liu and Matthew Schrecker",

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doi = "10.1137/24M1653240",

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T1 - Converging/Diverging Self-Similar Shock Waves

T2 - From Collapse to Reflection

AU - Jang, Juhi

AU - Liu, Jiaqi

AU - Schrecker, Matthew

PY - 2025/2/28

Y1 - 2025/2/28

N2 - We solve the continuation problem for the nonisentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar Güderley imploding shock solutions for a perfect gas with adiabatic exponent γ ∊ (1, 3] admit a self-similar extension consisting of two regions of smooth flow separated by an outgoing spherically symmetric shock wave of finite strength. In addition, for γ ∊ (1, 5 3 ], we show that there is a unique choice of shock wave that gives rise to a globally defined self-similar flow with physical state at the spatial origin.

AB - We solve the continuation problem for the nonisentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar Güderley imploding shock solutions for a perfect gas with adiabatic exponent γ ∊ (1, 3] admit a self-similar extension consisting of two regions of smooth flow separated by an outgoing spherically symmetric shock wave of finite strength. In addition, for γ ∊ (1, 5 3 ], we show that there is a unique choice of shock wave that gives rise to a globally defined self-similar flow with physical state at the spatial origin.

KW - compressible fluid flow

KW - nonisentropic Euler system

KW - radial symmetry

KW - shock wave

KW - similarity solutions

UR - https://www.scopus.com/pages/publications/85214923090

U2 - 10.1137/24M1653240

DO - 10.1137/24M1653240

M3 - Article

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VL - 57

SP - 190

EP - 232

JO - Siam Journal on Mathematical Analysis

JF - Siam Journal on Mathematical Analysis

IS - 1

ER -

Converging/Diverging Self-Similar Shock Waves: From Collapse to Reflection

Abstract

Funding

Keywords

ASJC Scopus subject areas

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Shock Waves in Gas Dynamics

Cite this

Converging/Diverging Self-Similar Shock Waves: From Collapse to Reflection

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Shock Waves in Gas Dynamics

Cite this