Lattice Boltzmann Methods for Compressible Two-Phase Flow Problems

By a combination of well-established mathematical techniques, it is possible to construct a general numerical method for solving any hyperbolic system of conservation laws with the following interesting features: time-explicit, unconditionally stable, accepting unstructured arbitrary meshes, of arbitrary order and naturally parallel. We give an overview of the construction of the method and an example of application to a multiphase compressible flow sedimentation problem.