Abstract: A continuous flux splitting method for unsteady Euler equations based on time-dependent body fitted coordinates is given. And with this method, an implicit difference equation for solving the unsteady transonic flow with Euler equations is established. In order to reduce the computer time for solving the block-matrix equations, the characteristic matrix transformation is used. This transformation does not change the discrete order of the equations but the CPU for solving the matrix equations can be reduced greatly. The numerical computation is made in the moving coordinates, so that not only the boundary conditions are kept on the real body surface, but the time-dependent body fitted coordinates are built in a very simple way as well. The NACA64A-10 airfoil which oscillates in pitching about its 1/4 chord point is computed. The computed results are in good agreement with the experiment data. Besides, some calculated results for the airfoil oscillating in heaving and both in heaving and pitching are also shown in the paper.

Key words: unsteady flow, flux splitting, Euler equation, transonic flow