Characteristic-based volume penalization-imposed wall function method for turbulent boundary layer modeling

A method to approximate near-wall boundary conditions for the compressible Reynolds-averaged Navier–Stokes equations is proposed. The differential formulation to match the external and the wall function solutions is reformulated in a form of the generalized characteristic-based volume penalization method to model the transfer of the shear stress from the outer region of the boundary layer to the wall. The exchange location is specified implicitly in terms of a localized source term in the boundary layer equation written as a function of the distance from the wall normalized by the viscous length scale. The shear stress on the wall is determined by solving an auxiliary equation for the wall-stress imposing the analytical wall function solution through the characteristic-based volume penalization method. The proposed method noticeably reduces the near-wall mesh resolution requirements without a significant modification of the numerical algorithm and completely eliminates the ill-defined explicit solution matching procedure. The developed approach is numerically implemented using the vertex-centered control volume method on structured meshes. Its effectiveness is demonstrated by solving two test problems: the two-dimensional channel flow and turbulent flow over an infinitely thin plate.