The NUmerical Osciliations Caused by the Boundaries Treatments in the Solution of the Euler Quasi-One-Dimensional Model

摘要

This paper deals with the numerical oscillations in the solution of the compressible, unsteady and quasi-one-dimensional model of Euler governing the subsonic flow inside a portion of a duct with non-physical boundaries. The presence of these oscillations is particularly obvious in the solution of a real flow where the boundary conditions are taken by measurements in an intake apparatus of a reciprocating engine. No absorbent boundary treatment is allowed because a time dependent solution is searched. Each boundary could be considered as an acoustical source. The resolution is done with the finite difference schemes of Lax-Wendroff or Harten-Roe (TVD). The diagnostic is done by observing the numerical resolution of a progressive acoustical pulsation in a subsonic steady flow whose analytical solution is known as been the solution of the equation of Pridmore-Brown. We explain how these oscillations take place at the entrance boundary and the roles of the resolution scheme and the scheme of establishment of the numerical boundary conditions. The physical boundary condition at the exit induce the trapping of the residual waves at the origin of these oscillations. The behavior of these ones is also interpreted. We also explain the presence of an entropic perturbation in the solution.