Non-weak/strong solutions in gas dynamics: A C~(11) p-version STLSFEF in eulerian frame of reference using p, u, p prmitive variables

摘要

Dimenwsionless forms of Navier-Stokes equations are derived in matrix form directly from conservation laws for one-dimensional transient compressible flow using primitive variables p, u, p. We construct p-version speae-time least squares finite element formulaton (STLSFEF) of the GDE in original parabolic form (i.e. no auxiliary variables or weak forms) in Lagrangian frame of reference using C~(11) type p-version herarchical interpotations. Time-marching procedure is used to compute time evolutions of subsequent spec-time strips. It is demonstrated that numerical solutions of Navier-Stoekes equations for high speed gasdynamics for isentropic and non-isentropic shocs is possible to compute without assumptions or approximations. Thime accurate numerical studies show resolution of the shock structure (i.e. shoick speed, shock whidth and shock relations) to be in excellent agreement with the anaytical solutions. The role and influence of artificial viscosity and thermal conductivity on shock structure is deonstrated. Compuression of air in a cylinder by a moving piston is modelled. True time evlutions are reported until steady shock conditions are achieved. The oreer os continuity of dependent variables, in the element interpolations are in agreement with the strong solutions of the GDE. When computed error functionals become zero (numerically) computed solutions have exactly the same characteristics as the strong solutions of the gas dynamics equations.