Front tracking and two-dimensional Riemann problems
The so-called method of front tracking is applied to several computation examples of jump discontinuities. Front tracking may be described as follows. A special grid is placed onto the discontinuity and equations are set up to propagate normally and tangentially to the wave front. This approach works away from the points where the discontinuity curves meet. Therefore main interest is drawn to different types of front intersection points described by the introduced new grid variables. Problems under consideration are the regular reflection of shock waves, Mach reflection of shock waves, a classification of two-dimensional elementary waves and conjections concerning Riemann problems. The behaviour of shock waves, contact discontinuities and rarefaction waves at the intersection points is discussed. Results of numerical computation examples are presented. From the mathematical point of view nonlinear hyperbolic systems of partial differential equations are under consideration such as the Euler equations for supersonic flow of a compressible, inviscid, polytropic gas. The mathematical foundations of the method of front tracking, however, one has to take from the literature quoted.
scientific article; zbMATH DE number 4027058