An Explicit Multi-Model Compressible Flow Formulation Based on the Full Potential Equation and the Euler Equations on 3D Unstructured Meshes

The development of a multi-model formulation to simulate three dimensional compressible flows on parallel computers is presented. The goal is to reduce the overall time and memory required to simulate the flow by using locally selected cheaper and more computational efficient physical models without sacrificing the global fidelity of the simulation. Our approach involves splitting the computational domain into different fluid flow regions and using the full potential model instead of the Euler or Navier-Stokes equations in regions where this approximation is valid. We show numerically that solving the full potential equation in regions of irrotational flow is not only more efficient but also improves the accuracy; avoiding any numerical generation of entropy. The main considerations addressed in this paper are the full potential and the Euler coupling and the discretization of the interface conditions between these domains. We use a fully unstructured finite volume discretization for both the full potential and the Euler equations, and the interface condition is derived by imposing the discrete conservation laws in the control volumes shared by both flow regions. 3D transonic flow simulations around a NACA0012 airfoil are investigated. Numerical simulations of fluid flow have sufficiently matured to be considered accurate for engineering design and analysis. However, for large scale simulations, the response time remains too large for the software to be used as an interactive tool even on the lastest supercomputers. While parallel computing reduces computation time proportionally to additional computational resource,