AN APPLICATION OF NONLOCAL EXTERNAL CONDITIONS TO VISCOUS-FLOW COMPUTATIONS

We are looking for a steady-state solution of an external flow problem originally formulated on an unbounded domain. Our case is a 2D viscou s compressible flow past a finite body (airfoil). We truncate the orig inal domain by introducing a finite grid around the airfoil and integr ate the Navier-Stokes equations on this grid with the help of a finite -volume code which involves a multigrid pseudo-time iteration techniqu e for achieving a steady state. To integrate the Navier-Stokes equatio ns on a finite subregion of an original domain only we supplement the numerical algorithm by special nonlocal artificial boundary conditions formulated on an external boundary of the finite computational domain . These artificial boundary conditions are based on the difference pot entials method proposed by V. S. Ryaben'kii. We compare the results pr ovided by the nonlocal conditions with those obtained from the standar d external conditions which are based on locally one-dimensional chara cteristic analysis at inflow and extrapolation at outflow. It turns ou t that the nonlocal artificial boundary conditions accelerate the conv ergence by about a factor of 3, as well as allow one to shrink substan tially the computational domain without loss of accuracy. (C) 1995 Aca demic Press. Inc.