Numerical comparison of unsteady compressible viscous flow in convergent channel

summary:This study deals with a numerical solution of a 2D flows of a compressible viscous fluids in a convergent channel for low inlet airflow velocity. Three governing systems -- Full system, Adiabatic system, Iso-energetic system$ based on the Navier-Stokes equations for laminar flow are tested. The numerical solution is realized by finite volume method and the predictor-corrector MacCormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. The unsteady grid of quadrilateral cells is considered in the form of conservation laws using Arbitrary Lagrangian-Eulerian method. The numerical results, acquired from a developed program, are presented for inlet velocity $\hat u_{\infty}=4.12 {\rm ms^{-1}}$ and Reynolds number Re = $4 \times 10^3$.