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TVD algorithms for the solution of the compressible Euler equations on unstructured meshes
Author(s) -
Lyra P. R. M.,
Morgan K.,
Peraire J.,
Peiró J.
Publication year - 1994
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.1650190906
Subject(s) - inviscid flow , euler equations , polygon mesh , stencil , discontinuous galerkin method , finite element method , compressible flow , euler's formula , mathematics , computation , compressibility , algorithm , computational science , computer science , geometry , mathematical analysis , classical mechanics , physics , mechanics , thermodynamics
The Galerkin finite element method is used as the basis for the construction of schemes for the solution of the two‐dimensional compressible Euler equations on unstructured triangular grids. The use of a side‐based data structure readily allows for the construction of a local (structured) stencil and the incorporation of a high‐resolution shock‐capturing method formulated within the TVD concept. The essential features of the finite element side‐based scheme and the ID TVD approach are described and their numerical implementation is discussed. The choice of limiters and the support for their computation are analysed and the solutions of some inviscid flows, obtained by advancing explicitly in time, are presented.