Adaptive strategy of transonic flows over vibrating blades with interblade phase angles

An error indicator and a locally implicit scheme with anisotropic dissipation model on dynamic quadri- lateral-triangular mesh are developed to study transonic flows over vibrating blades with interblade phase angles. In the Cartesian co-ordinate system, the unsteady Euler equations with moving domain effects are solved. The error indicator, in which unified magnitudes of dynamic grid speed, substantial derivative of pressure, and substantial derivative of vorticity magnitude are incorporated to capture the unsteady wave behaviours and vortex-shedding phenomena due to unsteadiness. To assess the accuracy of the locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, two flow calculations are performed. Based on the comparison with the related numerical and experimental data, the accuracy of the present approach is confirmed. According to the high-resolutional result on the adaptive mesh, the unsteady pressure wave, shock and vortex-shedding behaviours are clearly demonstrated.