Preprint 2003-002

A Lagrangian Discontinous Galerkin Type Method on Unstructured Meshes to Solve Hydrodynamics Problems

R. Loubere, J. Ovadia, and R. Abgrall

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 process is performed with a particle method: this remeshing is locally conservative and its accuracy can be adapted to the accuracy of the numerical method.

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R. Loubere <>
J. Ovadia <>
R. Abgrall <>
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<> January 5 2003.

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