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Pressure‐based adaption indicator for compressible euler equations
Author(s) -
Dewar Jeremy,
Kurganov Alexander,
Leopold Maren
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21970
Subject(s) - classification of discontinuities , euler equations , mathematics , robustness (evolution) , nonlinear system , compressibility , semi implicit euler method , backward euler method , residual , partial differential equation , compressible flow , flux limiter , limiter , euler's formula , shock wave , mathematical analysis , algorithm , computer science , mechanics , telecommunications , biochemistry , chemistry , physics , quantum mechanics , gene
We consider the Euler equations of gas dynamics and develop a new adaption indicator, which is based on the weak local residual measured for the nonconservative pressure variable. We demonstrate that the proposed indicator is capable of automatically detecting discontinuities and distinguishing between the shock and contact waves when they are isolated from each other. We then use the developed indicator to design a scheme adaption algorithm, according to which nonlinear limiters are used only in the vicinity of shocks. The new adaption algorithm is realized using a second‐order limited and a high‐order nonlimited central‐upwind scheme. We demonstrate robustness and high resolution of the designed method on a number of one‐ and two‐dimensional numerical examples. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1844–1874, 2015