The discontinuous Galerkin method allows a straightforward construction of efficient high-order methods on generally arbitrary grids for hyperbolic partial differential equations (PDEs) such as the Euler equations. However, hyperbolic PDEs admit discontinuities in the solution, even if the initial solution is smooth and it is well known that high-order schemes induce oscillations at discontinuities, called Gibbs phenomena. Hence, adequate numerical schemes are necessary to detect and handle discontinuities, ranging from shock fitting to shock capturing approaches. Recently, an entropy stable shock capturing method based on a convex blending of a low-order finite volume and a high-order discontinuous Galerkin method has been proposed, exploiting the fact that a high-order summation-by-parts operator can also be written in the form of a conservative finite volume scheme. In this talk, an extension of this entropy stable shock capturing scheme to moving meshes is proposed. The mesh movement is based on the arbitrary Lagrangian–Eulerian method. The freestream preservation and high-order convergence properties of the resulting scheme are demonstrated. Finally, the scheme is applied to a transonic compressor cascade laden with solid particles, where the mesh movement is induced by particle impacts, demonstrating its efficiency and capabilities.