An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry

In this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z   axis (i.e. all the functions do not depend explicitly on the angular variable θθ), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific upwinding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity uθuθ.