Non-Equilibrium Turbulence Modeling for High Lift Aerodynamics

This phase is discussed in ('Non linear kappa - epsilon - upsilon(sup 2) modeling with application to high lift', Application of the kappa - epsilon -upsilon(sup 2) model to multi-component airfoils'). Further results are presented in 'Non-linear upsilon(sup 2) - f modeling with application to high-lift' The ADI solution method in the initial implementation was very slow to converge on multi-zone chimera meshes. I modified the INS implementation to use GMRES. This provided improved convergence and less need for user intervention in the solution process. There were some difficulties with implementation into the NASA compressible codes, due to their use of approximate factorization. The Helmholtz equation for f is not an evolution equation, so it is not of the form assumed by the approximate factorization method. Although The Kalitzin implementation involved a new solution algorithm ('An implementation of the upsilon(sup 2) - f model with application to transonic flows'). The algorithm involves introducing a relaxation term in the f-equation so that it can be factored. The factorization can be into a plane and a line, with GMRES used in the plane. The NASA code already evaluated coefficients in planes, so no additional memory is required except that associated the the GMRES algorithm. So the scope of this project has expanded via these interactions. . The high-lift work has dovetailed into turbine applications.