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

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.