This paper reports the development of a third-order discontinuous Galerkin (DG) method for supersonic inviscid flow on a moving grid, as well as simulations of a simple model of crypto-steady supersonic pressure exchange (CSSPE) by solving 2D inviscid Euler equations. A total variation bounded (TVB) limiter is implemented for shock capturing. The third-order DG method is firstly validated using a case of supersonic vortex flow. Subsequently, the method is successfully employed to predict the crypto-steady supersonic flat-plate flow under various pressure ratios. In particular, at high pressure ratios between primary gas and secondary gas, a detached shock away from the trailing edge of the flat plate is accurately predicted. This study is our first step in approaching to developing a 3D numerical tool and modeling a novel pressure-exchange ejector.

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