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Non‐oscillatory shock‐capturing finite element methods for the one‐dimensional compressible Euler equations
Author(s) -
Yang J. Y.,
Lien FueSang,
Hsu ChangAn
Publication year - 1990
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.1650110405
Subject(s) - euler equations , mathematics , total variation diminishing , mathematical analysis , finite element method , classification of discontinuities , semi implicit euler method , backward euler method , riemann problem , euler's formula , compressible flow , shock (circulatory) , compressibility , riemann hypothesis , physics , mechanics , thermodynamics , medicine
A class of shock‐capturing Petrov–Galerkin finite element methods that use high‐order non‐oscillatory interpolations is presented for the one‐dimensional compressible Euler equations. Modified eigenvalues which employ total variation diminishing (TVD), total variation bounded (TVB) and essentially non‐oscillatory (ENO) mechanisms are introduced into the weighting functions. A one‐pass Euler explicit transient algorithm with lumped mass matrix is used to integrate the equations. Numerical experiments with Burgers' equation, the Riemann problem and the two‐blast‐wave interaction problem are presented. Results indicate that accurate solutions in smooth regions and sharp and non‐oscillatory solutions at discontinuities are obtainable even for strong shocks.