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We report the detailed information of a purely elastic instability and its mixing enhancement effect in a viscoelastic fluid flow driven by a constant pressure gradient along a curvilinear channel obtained for the first time from the three-dimensional direct numerical simulations (DNSs) of this kind of flow geometry.Three-dimensional unstable flow structures similar to those visualized in experiments are realized through the DNSs.The inception of elastic instability,conformation of microstructures,statistical and dynamic information of velocity field and the mixing enhancement effect caused by elastic instability are then discussed.