Uncertainty Quantification for Production Navier-Stokes Solvers

The uncertainty quantification methods developed under this program are designed for use with current state-of-the-art flow solvers developed by and in use at NASA. The Phase I program demonstrated the CRISP CFDREG error quantification and reduction code with simulations conducted using the NASA unstructured solvers FUN3D and USM3D. Phase I provided evidence supporting the suspected need for an error prediction code that matches the finite volume scheme of the Navier-Stokes solver itself. Phase II will continue this work by expanding our Error Transport Equation (ETE) solver to treat both classes of unstructured grid finite volume schemes. Support for the CGNS standard will be implemented and permit use of the Phase II product by a broader spectrum of potential users. Specific issues that affect numerical accuracy of the error predictions and how they propagate into integrated quantities such as lift and drag coefficients will be addressed. Reduction of error for large scale meshes is a matter of equal importance, and improvements are planned that will provide for anisotropic grid refinement within the existing CRISP CFDREG mesh adaptation code. Finally, error quantification approaches for transient applications will be explored to expand these developments to problems that involve inherent unsteadiness and/or moving boundaries.

NASA-developed Navier-Stokes solvers are heavily used by a number of private companies and organizations within the aerospace and defense industries. Engineers at these corporations and government laboratories rely on the accuracy of NASA CFD tools in the development of small business jets, commercial airliners, and next generation fighter aircraft. Error quantification is a necessity widely recognized by this community, and providing adequate grid resolution is a perennial challenge. To date, research in error quantification has largely been limited to academic research groups and government laboratories, and no commercially available package for error quantification and reduction currently exists. This offers a unique opportunity to assume the leading role as the first player in the market for such software. Outside of the aerospace and defense sectors, the proposed error quantification research finds ready application in the areas of biofluid flows, automobile engines, power generation and turbomachinery, chemical processing, etc.

The proposed research is directly relevant to the application of CFD analysis to aircraft and re-entry vehicles of current and future interest to NASA. CFD simulations are playing an increasing role in air vehicle analysis and design assessment, and numerical predictions often supplement the databases obtained in ground and flight tests. The proposed research will impact the use of CFD analysis tools by NASA personnel in verifying the accuracy of force and moment predictions, surface pressures, heat flux distributions, etc., providing not only numerical error bars and certifiable confidence levels in simulated results, but also quantifiable reduction of error through automated mesh modification. As the research effort addresses fundamental issues in numerical simulation accuracy, numerous applications of interest to NASA exist. Potential applications of the proposed error quantification and reduction research include simulation of launch vehicles, planetary re-entry capsules, attitude control jets, liquid fuel feed systems, rocket nozzle performance, etc.

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