Solution of the Noh problem using the universal symmetry of the gas dynamics equations

Scale Invariance of the Homentropic Inviscid Euler Equations with Application to the Noh Problem

“…First introduced by W. Noh in 1987 [4], the Noh problem has become "the workhorse of compressible hydrocode verification for over three decades" [26]. Its distinguishing features, potential uses, advantages, disadvantages, physical implications, connections to other physical scenarios, possible generalizations, and a variety of related topics have been extensively documented; see Ramsey et al [25], Velikovich and Giuliani [26], and references therein for additional details.…”

“…Conditions for the existence of semi-analytic or even closed-form solutions to the classical Noh problem in any of the 1D geometries (i.e., n = 0, 1, or 2) have been discussed at length by Axford [51], Ramsey et al [25], Burnett et al [8], and Velikovich and Giuliani [26]. The existence of the 1D planar (n = 0) solutions is a direct consequence of arguments advanced by Courant and Friedrichs [52] and Menikoff and Plohr [5] for generalized Riemann problems, though these arguments can also be cast in terms of the universal symmetries inherent Eqs.…”

“…• Employ an EOS allowing for a simultaneous constant pressure and non-constant density state. Several examples of EOS closure laws featuring this property are provided by Axford [51], Ramsey et al [25], and Burnett et al [8].…”

“…This behavior is distinct from that encountered in the classical ideal gas Noh problem, which features a maximum shock compression limit independent of u 0 . Following from the definition of the ideal gas entropy given by Zel'dovich and Raizer [22], and the classical 1D planar ideal gas solution disseminated by Ramsey et al [25], the entropy in the shocked region for this case is given by…”

“…Morever, a second goal of this work is to leverage the symmetry analysis results to construct piecewise homentropic analogs of classical solutions of the inviscid Euler equations: for example the Noh stagnation shock problem. Some work along these lines has recently been performed by Ramsey et al [25], Burnett et al [8], Velikovich et al [26], and Deschner et al [27]. The motivation for selecting a Noh problem for demonstration purposes is thus to enable comparison to this wide body of existing work.…”