21st Congress of International Council of the Aeronautical Sciences, Melbourne, Australia, 13-18 September, 1998
Paper ICAS-98-7.4.4

NON-REFLECTING BOUNDARY CONDITIONS FOR NON-LINEAR EULER CALCULATIONS USING AN IMPLICIT APPROACH

Tchernycheva O. V.
Royal Institute of Technology, Sweden

Keywords: non-reflecting boundary conditions, non-linear euler calculations, implicit approach

In numerical calculations of the flow through turbo machinery blade rows, it is often essential to introduce artificial boundaries to limit the area of computation. These artificial boundaries and boundary conditions must affect the solution in a manner such that it closely approximates the free space solution which exists without these boundaries. In practical, it means that the amplitudes of waves reflected from these artificial boundaries have to be minimized and hopefully eliminated. In concept, they correspond to the nonreflecting boundary conditions used in time linearized methods. Accurately predicting the behavior of complex unsteady flows with explicit computational analysis can require enormous computer resources. In order to decrease it and make the solver feasible for single processor use different methods are used. Implicit numerical analysis and dual time step marching are some of them. In the present paper, numerical solutions are presented for two-dimensional Eulerian gas-dynamic equations using an implicit approach for the flow field and for the boundary conditions. For the field a first order implicit scheme of Beam-Warming type on a second order Van Leer flux vector splitting is used. The boundary conditions are based on the characteristic form of the linearized Euler equations. With selected test cases, the importance of a correct simulation of the boundary conditions for stability margin of the blade rows is clearly demonstrated. It is shown that the result of numerical flow calculations is depend more on quality of boundary conditions, and less on the size of computational domain.

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