Numerical solution of the unsteady Euler equations for airfoils using approximate boundary conditions

This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary rectilinear grids. Boundary conditions on the surface of an airfoil are implemented by using their first-order expansions on the mean chord line. The method is not restricted to flows with small disturbances since there are no restrictions on the mean angle of attack of the airfoil. The mathematical formulation and the numerical implementation of the wall boundary conditions in a fully implicit time-accurate finite-volume Euler scheme are described. Unsteady transonic flows about an oscillating NACA 0012 airfoil are calculated. Computational results compare well with Euler solutions by the full boundary conditions on a body-fitted curvilinear grid and published experimental data. This study establishes the feasibility for computing unsteady fluid-structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in saving computer time and program design since it does not require the generation and implementation of time-dependent body-fitted grids.