An Application of Nonlocal External Conditions to Viscous Flow Computations

Abstract

We are looking for a steady-state solution of an external flow problem originally formulated on an unbounded domain. Our case is a 2D viscous compressible flow past a finite body (airfoil). We truncate the original domain by introducing a finite grid around the airfoil and integrate the Navier-Stokes equations on this grid with the help of a finite-volume code which involves a multigrid pseudo-time iteration technique for achieving a steady state. To integrate the Navier—Stokes equations 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 potentials method proposed by V. S. Ryaben'kii. We compare the results provided by the nonlocal conditions with those obtained from the standard external conditions which are based on locally one-dimensional characteristic analysis at inflow and extrapolation at outflow. It turns out that the nonlocal artificial boundary conditions accelerate the convergence by about a factor of 3, as well as allow one to shrink substantially the computational domain without loss of accuracy.