Shock wave detection in two-dimensional flow based on the theory of characteristics from CFD data

Abstract

A method to detect the discontinuity of a shock wave from computational fluid dynamics (CFD) data was developed based on the theory of characteristics and was adopted to replace the inaccurate method that involves observation of the location of steep spatial gradient with respect to the primitive variables, such as pressure. A shock wave is mathematically defined as a convergence of characteristics, in which each type of Riemann invariant is conserved within each characteristic. In the vector field of the characteristics, such convergences are interpreted as critical lines of the streamlines, which are easily identified by calculating the eigenvectors of the vector field of propagation velocity of the Riemann invariant. The use of a triangular cell system enables unique determination of the linearized vector field in each cell and enables analytical identification of the critical line within this field. Shock waves can be successfully extracted using this method. The method can be extended to the detection of moving shock waves by considering the coordinate moving with the shock.