Adjoint-based optimization of a source-term representation of vortex generators

An optimization approach is presented that can be used to find the optimal source term distribution in order to represent a high-fidelity vortex-generator (VG) induced flow field on a coarse mesh. The approach employs the continuous adjoint of the problem, from which an exact sensitivity is calculated and used in combination with a trust-region method to find the source term which minimizes the deviation with respect to the reference velocity field. The algorithm is applied to an incompressible flow over a rectangular VG and VG pair on a flat plate and compared to results obtained with the jBAY-model and a body-fitted mesh simulation. The results indicate that a highly accurate flow, yielding only minimal errors with respect to the shape factor, circulation and vortex core, can be obtained on coarse meshes when adding a source term to only a limited number of cells. This approach therefore demonstrates the potential of source-term models to include the effects of VGs in computations of large-scale geometries. It also allows quantification of the achievable accuracy on a particular mesh and the calculation of the source term which is optimal for a specific situation. Furthermore, the optimization approach can be used to diagnose the deficiencies of an existing source-term VG model, in this work the jBAY model.