ARTIFICIAL BOUNDARY-CONDITIONS FOR COMPUTATION OF OSCILLATING EXTERNAL FLOWS

In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible vi scous plane flow past a finite body (airfoil). Oscillations of the flo w in time may be caused, for example, by the time-periodic injection o f fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To con duct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boun dary and to further consider only a finite computational domain. Conse quently, we will need to formulate some artificial boundary conditions (ABCs) at the introduced external boundary. The ABCs we are aiming to obtain must meet the following fundamental requirement. One should be able to uniquely complement the solution calculated exterior so that the original problem is solved within the desired accuracy. Our constr uction of such ABCs for oscillating flows is based on an essential ass umption: the Navier-Stokes equations can be linearized in the far fiel d against the free-stream background. To actually compute the ABCs, we represent the far-field solution as a Fourier series in time and then apply the difference potentials method (DPM) of V. S. Ryaben'kii. Thi s paper contains a general theoretical description of the algorithm fo r setting the DPM-based ABCs for time-periodic external flows. Based o n our experience in implementing analogous ABCs for steady-state probl ems (a simpler case), we expect that these boundary conditions will be come an effective tool for constructing robust numerical methods to ca lculate oscillatory flows.