A method for simulations of the two-dimensional compressible flow in aerodynamically highly loaded turbomachinery on unstructured adaptive grids is presented in this paper. The discretization of the conservative laws in space is executed by the finite volume method. For high efficiency an implicit solution procedure is used. The flux vector of the inviscid flow is calculated by a modified difference splitting method described by Reichert and Simon (1994). To predict the turbulent flow an explicit algebraic stress model in conjunction with k and ε equations is used (Lenke and Simon, 1997). Both for the generation of the initial grid as well as for the grid adaptation the same algorithm is used which is based on the advancing-front method according to Peraire et.al. (1987). For the simulation of high Reynoldsnumber flow within thermal turbomachinery it is most favorable to use quadrilateral elements in the boundary layers in addition to the triangular elements in the main flow region. To adapt the so-called combined grids, some kind of key variables are chosen, e.g. change in total pressure in combination with a shock detector.

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