Boundary Conditions

Boundary conditions have always been a critical issue in the use of DNS. Specifying boundary conditions at open boundaries is a difficult issue. For incompressible flows, statistically homogeneous directions such as the spanwise direction in a 2-D boundary layer are straightforward to treat and periodic conditions are imposed. However, most fully developed complex flows are inhomogeneous in the streamwise direction, which require both inflow and outflow boundary conditions to be specified.

Compressibility introduces additional boundary condition issues. Characteristic analysis must be used in compressible DNS to determine the number of boundary conditions required.

In the far-field, disturbances are generally assumed to vanish, so either homogeneous Dirichlet or exponentially decaying boundary conditions have been used. But these assumptions can lead to considerable errors when the nonlinear effects are large and the mean-flow distortion quantity is important.