Abstract
Abstract
Accurately tracking the propagation process of a wave front is important for studying the propagation law of shock waves. In this study, a novel arc-length numerical algorithm to effectively calculate the interruption of shock waves is proposed, and a systematic theoretical analysis and application of this research are conducted. First, the arc-length numerical method is proposed based on the hyperbolic conservation model equation, and the basic concept of the arc-length numerical method of hyperbolic problems is provided. Then, an introduction method for arc-length in multidimensional space is described from the perspective of tensor analysis, and the mathematical model of shock wave propagation problems in arc-length space is established. The discrete solution of the spatial mathematical model of arc length is given, and control and smoothing factors are added to ensure shock wave propagation without oscillation. Finally, the numerical calculation of the Lax and double Mach reflection problems shows that the arc-length numerical algorithm can be widely used as a new calculation method for shock interruption problems.