A Lagrangian Discontinuous Galerkin‐type method on unstructured meshes to solve hydrodynamics problems | Zendy

Loubère R. | Zendy; Ovadia J. | Zendy; Abgrall R. | Zendy

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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

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.

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