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Section: New Results

Discontinuous Galerkin methods for compressible multiphase flows

Participants : Vincent Perrier, Erwin Franquet.

We developed discontinuous Galerkin methods for compressible multiphase flows. This method is based on the method developed in [12] concerning the modelling of multiphase flows, and on the method developed in [36] concerning multiphase flows. In the method developed in [12] , the exact expression of the continuous system is unclear, and as a consequence, the cell integral that naturally appear in the discontinuous Galerkin formulation is not clearly defined. In [2] , [11] , we developed an original analysis of the scheme [12] by mean of a stochastic process, which gave a unified framework for defining both the numerical scheme and the continuous limit. This was then applied to multiphase flows with phase transition in [10] , [1] . Our method is currently being extended to interface flows with the maximum preserving limiter developed by [38] .