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Entropy correcting schemes and non‐hierarchical auto‐adaptive dynamic finite element‐type meshes: Applications to unsteady aerodynamics
Author(s) -
Richter Roland,
Leyland Pénélope
Publication year - 1995
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.1650200811
Subject(s) - inviscid flow , euler equations , polygon mesh , aerodynamics , adaptive mesh refinement , upwind scheme , compressible flow , finite element method , euler's formula , entropy (arrow of time) , mesh generation , mathematics , computer science , algorithm , compressibility , mathematical optimization , mathematical analysis , geometry , computational science , mechanics , physics , quantum mechanics , discretization , thermodynamics
This paper discusses the different sources of non‐physical entropy production which occur in the numerical resolution of the Euler equations for compressible inviscid flow and proposes several ways of correcting these effects. In particular a hybrid corrected centred, augmented by an accurate upwind scheme near singular boundaries is proposed which satisfies the mathematical entropy condition, and which solves the flow accurately within regions near non‐smooth boundaries of the computational domain. A coupled new dynamic auto‐adaptive mesh algorithm which produces highly accurate solutions is also introduced. This algorithm is non‐hierarchical. i.e. it does not depend on a fixed background mesh, which allows structural and geometrical changes and generates extremely precise discretizations for steady and unsteady flow.