Exact linear far-field conditions for three-dimensional aerodynamic stationary transonic flows

We consider the problem of imposing artificial boundary conditions on the external boundary of a computational domain for stationary aerodynamic transonic flow simulation. The proposed construction of nonlocal boundary conditions is based on the assumption that outside a computational domain the flow is governed by the Euler equations linearized about the free-stream subsonic uniform background; this model can treat flows with wakes admitting nonzero vorticity and nonconstant entropy at the outflow. We use potential theory in order to find the desired conditions which are nonlocal and exact with respect to the considered model. The nonlocal operator modelling the boundary conditions requires only the evaluation of two surface integrals throughout the artificial boundary. We discuss briefly some questions of the numerical implementation of the proposed conditions in the form of relaxation methods for finding the solution to a flow problem and estimate the required computational costs. Finally, we give some numerical results by testing the obtained computational formulae.