Non-reflecting Inflow and Outflow in a Wind Tunnel for Transonic Time-Accurate Simulation

We consider a time-dependent flow problem in an infinitely long wind tunnel of circular cross-section. It is assumed that beginning with a distance up- and downstream from the stream-lined body, the flow is approximately described by the time-dependent Euler equations linearized about a uniform free-stream flow. By using this linear model, we transfer the boundary conditions from infinity to the front and back boundaries of a finite computational domain. The obtained bound- ary conditions called transparent ones TBCs.are represented by explicit formulae in the physical space. The TBCs contain operators of Fourier expansion with respect to eigenfunctions of the cross-section and convolutions with respect to time, i.e., they are non-local in both space and time. One possibility of their numerical implementation is described; the main attention is paid to the evaluation of the convolution operator. Due to the representation of the convolution kernel by an exponential polynomial, the evaluation formulae become even local in time.