Development of a RANS Based Wall-Model for Cartesian Grid Navier-Stokes Solvers

In this research effort, we are proposing the development of an advanced wall model for the numerical solution of the Reynolds Averaged Navier-Stokes (RANS) equations on Cartesian grids employing an immersed boundary method. Immersed boundary methods have drawn wide attention over the past decades as their volume mesh generation process can be fully- automated independent of the complexity of the geometry. Furthermore, the requirements for surface mesh quality within IBM approaches, in contrast to conventional body-fitted approaches, is significantly lower. The proposed research addresses the number one challenge for Cartesian mesh-based methods --- the inability to efficiently and accurately resolve the thin turbulent boundary layers encountered in high-Reynolds number flow applications. A new 3D ODE-based wall model (including pressure gradient and convective terms) will be developed and coupled with the higher-order IBM. This method provides the near-wall modeling for adaptive hybrid RANS-LES and WMLES approaches, as well as for pure RANS solvers. By employing a multi-resolution approach and hybrid programming paradigms this approach can meet the high-performance computing capabilities expected from modern simulation codes. Long term, the proposed research has the potential of being truly transformative because it will significantly accelerate CFD work flow and the degree of automation provided will extend the ability to conduct reliable, high-fidelity, turbulent flow simulations efficiently, and accurately, to a much broader user base. Furthermore, the methods developed in this research will be beneficial for multi-design analysis and optimization (MDAO) approaches, as well as for coupling with different physics solvers, such as those used for fluid-structure interaction.