An efficient hybrid difference scheme, based on the second-order time and spatial difference algorithms for solving the time-marching Navier-Stokes equations, was developed to simulate turbine cascade flow and heat transfer problems. The main feature of the present scheme is that the matrix-valued dissipation terms are incorporated into the time-derivative terms to form a time-dependent discretization scheme. The overall difference scheme consists of an explicit step in global time steps and an implicit step in each local time step. The viscous flux vectors are decomposed to simplify the flow calculation in the explicit step. In order to simplify the programming procedure and to save computational time, the two-sweep procedure was adopted in the implicit scheme instead of using traditional matrix operations. The numerical method proposed in this study comprises of the positive features of both explicit and implicit algorithms. The method was applied to calculate the flow around C3X and VKI cascades. The computed results were compared with experimental data as well as with computations solving by other schemes. It is demonstrated in this article that the computations obtained by using the present scheme show good agreement with both experiments and the computations obtained with other numerical schemes. [References: 20]
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