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Ghost cell boundary conditions for the Euler equations and their relationships with feedback control

pubblicazioni - Articolo

Ghost cell boundary conditions for the Euler equations and their relationships with feedback control

In this work we analyze some weakly imposed boundary conditions for the Euler Equations of gasdynamics. We prove that our particular scheme can be regarded as a proportional feedback control. Some numerical experiments are included.

Computational gasdynamics _nds many applications in engineering ranging from the optimization of rocket nozzles to the study of airfoils. As a consequence, the numerical solution of the Euler equations using the _nite volume method is very popular as a standard computing tool. One of the most tricky aspects in this kind of simulations is the imposition of the boundary conditions. Many approaches exist to tackle this problem and the ghost cell technique is one of the most applicable ones. In particular, this technique has already been used to enforce the wall boundary condition. In this paper the ghost cell technique is used to impose di_erent boundary conditions such as the inow, the pressure and the temperature ones. The merits of this technique are compared to other approaches and it is proved, under some simplifying hypotheses, that the ghost cell technique can be regarded as a local proportional feedback control. The stability and the performances of the control loop are investigated as well.

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