Numerical simulation of inviscid compressible flow through two-dimensional cascade by finite area method

The steady inviscid compressible flow through the two dimensional cascade is computed by the method of time-dependent finite area with hexagonal integral domain. Three different equation systems are considered which are physically equivalent under two assumptions: (1) steady state, (2) subsonic, or (3) existing weak shock flow field. The basic system is composed of the continuity equation, the Euler equation, and the energy equation. Their differences during numerical behavior approaching the steady state are examined through computations. To prevent the pressure or the density from becoming negative, the spatial averaging for smoothing was used, which appears to have some artificial viscosity and damping factor for time-dependent computations. In the steady state computed airfoil pressure distributions show good agreement with experimental measurements and there were few differences among the three equation systems.