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Mathematical models for inviscid and also viscous transonic flows through turbine cascades are presented. For numerical solution, finite volume upwind explicit (Runge-Kutta) and implicit (backward Euler) methods are considered. The flux splitting methods include AUSM, AUSMPW+ and HLLC Riemann solvers. The mathematical models are applied to flow through VKI and SE1050 turbine cascades.doi:10.1088/1742-6596/490/1/012093 fatcat:6azijilaw5d37d3codzhtjkiwi