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A Lagrangian Discontinuous Galerkin‐type method on unstructured meshes to solve hydrodynamics problems
Author(s) -
Loubère R.,
Ovadia J.,
Abgrall R.
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.665
Subject(s) - discontinuous galerkin method , polygon mesh , riemann solver , classification of discontinuities , mathematics , solver , lagrangian , stability (learning theory) , type (biology) , galerkin method , mathematical optimization , mathematical analysis , computer science , finite element method , geometry , finite volume method , physics , mechanics , machine learning , thermodynamics , ecology , biology
Abstract This paper concerns a new Lagrangian Discontinuous Galerkin‐type method to solve 2D fluid flows on unstructured meshes. By using a basis of Bernstein polynomials of degree m in each triangle, we define a diffusion process which ensures positivity and stability of the scheme. The discontinuities of the physical variables at the interfaces between cells are solved with an acoustic Riemann solver. A remeshing/remapping process is performed with a particle method: the remapping is locally conservative and its accuracy can be adapted to the accuracy of the numerical method. Copyright © 2004 John Wiley & Sons, Ltd.