Improved accuracy of incompressible approximation of compressible euler equations
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Cheng, Bin (2014) Improved accuracy of incompressible approximation of compressible euler equations SIAM Journal on Mathematical Analysis, 46 (6). pp. 3838-3864.
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Official URL: https://epubs.siam.org/doi/10.1137/140955173
Abstract
© 2014 Society for Industrial and Applied Mathematics.This article addresses a fundamental concern regarding the incompressible approximation of fluid motions, one of the most widely used approximations in fluid mechanics. Common belief is that its accuracy is O(ε), where ε denotes the Mach number. In this article, however, we prove an O(ε2) accuracy for the incompressible approximation of the isentropic, compressible Euler equations thanks to several decoupling properties. At the initial time, the velocity field and its first time derivative are of O(1) size, but the boundary conditions can be as stringent as the solid-wall type. The fast acoustic waves are still O(ε) in magnitude, since the O(ε2) error is measured in the sense of Leray projection and more physically, in time-averages. We also show when a passive scalar is transported by the flow, it is O(ε2) accurate pointwise in time to use incompressible approximation for the velocity field in the transport equation.
| Item Type: | Article | ||||||
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| Divisions : | Faculty of Engineering and Physical Sciences > Mathematics | ||||||
| Authors : |
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| Date : | 1 January 2014 | ||||||
| DOI : | 10.1137/140955173 | ||||||
| Copyright Disclaimer : | Copyright © by SIAM. Unauthorized reproduction of this article is prohibited | ||||||
| Uncontrolled Keywords : | Incompressible approximation; Compressible Euler equations; Convergence rates; Time-averages; Initial-boundary value problem; Singular limits; Multiscale PDEs; Hyperbolic PDEs | ||||||
| Depositing User : | Symplectic Elements | ||||||
| Date Deposited : | 29 Jul 2016 16:02 | ||||||
| Last Modified : | 16 Jan 2019 17:05 | ||||||
| URI: | http://epubs.surrey.ac.uk/id/eprint/811279 |
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