A staggered scheme for the compressible Euler equations on general 3D meshes (Q6571374)

The authors develop a velocity convection operator for space discretizations based on prismatic and pyramidal meshes, with the following degrees of freedom: the velocities are face-centred while the scalar variables are cell-centred. This operator takes a finite volume-like structure, with a finite volume approximation based on a dual mesh. The resulting operator is formulated in such a way that a local discrete kinetic energy identity is easily derived. For the solution of the Euler equations, this kinetic energy balance allows to construct a discrete internal energy equation which preserves the sign of the unknown and ensures that the scheme is consistent with the total energy balance, and thus captures the shock solutions. This process yields a consistent convection operator in the Lax-Wendroff sense. Some numerical tests are presented to confirm the expected scheme convergence, with a first-order rate on a pure shock solution.