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Development of an adaptive discontinuity‐capturing hyperbolic finite element model
Author(s) -
Fang C. C.,
Sheu Tony W. H.
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.677
Subject(s) - discontinuity (linguistics) , finite element method , euler equations , mathematics , galerkin method , matrix (chemical analysis) , euler's formula , adaptive mesh refinement , domain (mathematical analysis) , discontinuous galerkin method , taylor series , mathematical analysis , computer science , structural engineering , engineering , computational science , materials science , composite material
In this paper we present a five‐parameter Taylor–Galerkin finite element model to simulate Euler equations in a domain of two dimensions. The introduced free parameters are theoretically determined by employing M‐matrix theory to obtain a physically correct and non‐oscillatory solution in regions containing a sharp solution profile. To improve the computational efficiency and solution accuracy, grids are adaptively added to obtain solutions with fewer mesh points. The discontinuity‐capturing finite element model has been validated against test cases, reproducing analytical solutions to the gas dynamic problems under the current investigation. Copyright © 2004 John Wiley & Sons, Ltd.