Intrinsically Efficient and Accurate Viscous Simulations via Hyperbolic Navier-Stokes Systems
Technical Report,01 Aug 2012,31 Jul 2016
National Institute of Aerospace Associates Hampton United States
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Unstructured-grid methods are essential for computations with complex geometries such as rotorcraft simulations, but its potential has been limited by a higher cost than structured-grid methods as well as inaccuracy in gradient predictions e.g., diffused or oscillatory vorticity predictions. Grid irregularities are hard to avoid particularly once grid adaptation is performed, which is a critical technique especially for high-order unstructured-grids methods to be practical. Current state-of-the-art Navier-Stokes NS codes are known to produce highly erratic viscous stress and heating distributions. Resolution of these problems is very important for justifying the use of high-fidelity models in aerodynamic design and optimization. In this project, we address these issues by developing a Navier-Stokes solver based on a novel first order hyperbolic system method. The new solver is expected to yield O1h acceleration in convergence over existing solvers, where h is the typical grid spacing, as well as achieve high-accuracy in auxiliary quantities, viscous stresses, heating rates, and vorticity, on unstructured grids. These improvements will be achieved by the new method in which the Navier-Stokes equations are discretized as a first-order hyperbolic system including the auxiliary quantities as additional variables. The new code will enable complex large-scale simulations with the current hardware and meet the challenge of highly efficient and accurate multi-scale unsteady aerodynamic computations of Armys interest vortex-dominated flows, separated flows, wake interaction, and dynamic stall of rotor-craft, helicopter blades, high-speed missiles, gun-launched projectiles, micro air vehicles, and micro adaptive flow control, which require especially accurate vorticity predictions. The new solver is implemented in the framework of a practical flow solver used by Army, NASAs fully unstructured and parallel 3D RANS code, FUN3D.
- Numerical Mathematics