A method of three-dimensional curved characteristics for shock-flowfield reconstruction and analysis

The method of three-dimensional curved characteristics (MOTC), built upon the three-dimensional curved shock theory (3D-CST-boos), is developed to uncover the downstream flow physics of three-dimensional shock-dominated supersonic flows. Starting from the post-shock pressure gradients and streamline curvatures supplied by 3D-CST-boos at the shock surface, MOTC advances these quantities along streamlines and characteristics to construct the complete downstream flowfield. The methodology derives a comprehensive set of governing equations, including gradient terms, along streamlines and characteristics. A key advantage over conventional osculating methods lies in its retention of the lateral pressure gradient and cross-flow information, which substantially enhances the accuracy of three-dimensional flowfield simulations. The method is verified against inviscid CFD for both external and internal flow configurations, achieving errors below 0.5 %. More importantly, the retained gradient information reveals a cross-over of the streamwise compression: near the shock, the pressure gradient is governed by the transverse shock curvature; while further downstream, the lateral pressure gradient drives flow convergence or divergence, reversing the compression ordering across different shock geometries. The lateral pressure gradient distribution is controlled by the shock axial ratio, providing a guideline for shock shape selection in forebody or inlet design. For internal flows, the reflected shock asymmetry is governed by the same shock-curvature-to-transverse-flow transition, offering a physical basis for centre-body design. The combination of accuracy, computational efficiency and the ability to trace flow physics from the shock to the far-field positions MOTC as a powerful tool for analysis and inverse design of supersonic flowfields.