Abstract
We propose an explicit in time- discontinuous Galerkin scheme on moving grids using the arbitrary Lagrangian–Eulerian approach for one-dimensional Euler equations. The grid is moved with a velocity that is close to the local fluid velocity, which considerably reduces the numerical dissipation in the Riemann solvers. Local grid refinement and coarsening are performed to maintain the mesh quality and avoid very small or large cells. Second-, third-, and fourth-order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.
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