This paper presents a geometric variational discretization of compressiblefluid dynamics. The numerical scheme is obtained by discretizing, in astructure preserving way, the Lie group formulation of fluid dynamics ondiffeomorphism groups and the associated variational principles. Our frameworkapplies to irregular mesh discretizations in 2D and 3D. It systematicallyextends work previously made for incompressible fluids to the compressiblecase. We consider in detail the numerical scheme on 2D irregular simplicialmeshes and evaluate the scheme numerically for the rotating shallow waterequations. In particular, we investigate whether the scheme conservesstationary solutions, represents well the nonlinear dynamics, and approximateswell the frequency relations of the continuous equations, while preservingconservation laws such as mass and total energy.
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