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Automated Parametric Discretization Tool for High-Fidelity Hypersonic Design Analysis



OBJECTIVE: Take recent mathematical advances in use by the movie animation industry for creating subdivision surfaces and extend to three dimensions for use in CFD and CSM solvers to enable high-fidelity hypersonic vehicle design. 

DESCRIPTION: The current state of hypersonic computational fluid dynamic solvers being used by the Air Force, other DOD members, and NASA require structured order numerical methods to accurately predict aerodynamic performance and heat transfer for flight and reentry greater than Mach 6. This results in the requirement for generating structured meshes for computational fluid dynamics (CFD) and computational structure mechanics (CSM) solvers to capture the sharp gradients found in their solution. These types of grids allow for the required C1 (continuous in the first spatial derivatives) and C2 (continuous in the second spatial derivatives) continuity required by hypersonic CFD solvers. Tetrahedral mesh geometries although easy to create automatically have great difficulty in ensuring the C1 and C2 continuity throughout the entire solution domain. Making this one of the major causes of tetrahedral grid generation not working well for current industry CFD solvers used for hypersonic flow calculations. Current state of the art technology for structured mesh generation requires significant man hours that now take longer than the time CFD solvers use to compute hypersonic flows with the full Navier-Stokes equations. This significantly limits the capability of the high-fidelity analysis tools to impact the design cycle of hypersonic systems. Automation of the process to allow for seamless adaption to changes in the CAD (Computer Aided Design) definition of the hypersonic system are a requirement to close this gap. The animation industry has closed this gap in regards to model generation of movie characters and the actors controlling the motions of said characters. One example is the Pixar Opensubdiv library that automatically creates subdivision surfaces as the structured discretization domain for image rendering based off of parameterized character models. This surface rendering technology along with recent mathematical advances in creating a union between Non-Uniform Rational Basis Splines (NURBS) and sub-division geometry can finally allow for fully coupled definition between CAD software definitions and discretized definitions required by CFD solvers. The work to be conducted in this SBIR would be to fold these technologies into a grid generation software tool that is completely driven by parametric representation such as found in modern CAD software that will allow for easy exchange between the CAD and CFD/CSM environment. The tool should employ a smoothing strategy that guarantees C1 and C2 even for multi-point mesh singularities. The mesh should then be defined as parametric system. In addition, an external library with open source licensing is to be developed to allow automated creation of discretized domains for current CFD and CSM solvers from this parametric definition. This library must also create the grid in a partitioned distributed memory format compatible with CFD solvers that are utilized on large scale cluster systems. The CFD solver must then be allowed to communicate back discretization requirements that then the library will use to refine the solution domain and send it back to the CFD solver. This should also allow for user defined perturbations (control surface deflections or optimization corrections) to the underling parametric definition and automatically discretize the domain to this new requirement. 

PHASE I: Develop strategy for implementation of automated discretization process and survey CFD/CSM solvers to identify types of data memory formats required by CFD solvers to ensure compatibility. Outline initial math for representation of parametric volumes, surfaces and curves. Demonstrate discretization and smoothing methodology on curve and surface geometries. 

PHASE II: Extend methodologies developed in Phase I to volume geometries. Take government reference hypersonic vehicle CAD geometries defined by NURBS, generate parametric grid volume definition, and create distributed structured discretized domain holding C1 and C2 continuity. Demonstrate capability for grid refinement and perturbations to parametric definition of underlying CAD definition of hypersonic geometry. Develop external library for coupling to Navier-Stokes CFD solver. Demonstrate automated grid creation and execution of CFD solver. 

PHASE III: Commercialization of software and release of open source library for beta testing to small working group demonstrating capability on multiple hypersonic geometries. 



2:  McDonnell, K.T., et al. "Subdivision Volume Splatting," Eurographics/IEEE-VGTC Symposium on Visualization, 2007.

3:  Cashman T.J., "NURBS-compatible subdivision surfaces," University of Cambridge, Technical Report UCAM-CL-TR-733 (2010).

4:  Bajaj, C., et al. " A subdivision scheme for hexahedral meshes," The Visual Computer, 18, 343-356 (2002).


KEYWORDS: Computer Aided Design (CAD), Computational Fluid Dynamics (CFD), Computational Fluid Mechanics (CFM), Hypersonic, Vehicle Design, Computational Grids 

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