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In this study, a high order discontinuous Galerkin method for the two dimensional Euler equations is presented, the numerical method is constructed on unstructured hybrid mesh which contains both triangle and quadrangle elements, and the van leer Riemann solver is used for computing fluxes between elements. In this study, in order to handle curved geometry boundaries, high order curved elements are used to describe geometry boundaries and maintain the high order property of this method. A number of test cases are presented to demonstrate the accuracy of this method, the results of test cases show that when curved elements are utilized, the discontinuous Galerkin method could archive its designed order on domains with curved geometry boundaries.

discontinuous galerkin method; euler equations; hybrid mesh; curved element