Non‐weak/strong solutions in gas dynamics: a C¹¹p‐version STLSFEF in Lagrangian frame of reference using ρ, u, p primitive variables

In this paper, we present computations of the non‐weak solutions of class C 11 of transient Navier–Stokes equations for compressible flow in Lagrangian frame of reference using space‐time least squares finite element formulation with primitive variables ρ, u, p . For high speed compressible flows the solutions reported here possess the same orders of continuity as the governing differential equations. The role of diffusion i.e. viscosity (physical or artificial) and thermal conductivity on shock structure is demonstrated. Compression of air in a rigid cylinder by a rigid, massless and frictionless piston is used as a model problem. True time evolutions of class C 11 are reported beginning with the first time step until steady shock conditions are achieved. Comparisons with analytical solutions are presented when possible.