This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The principal investigator (PI) proposes to research mathematical models and numerical methods for enabling long time accuracy in turbulent fluid flow simulations. The first aspect is the development, through mathematical and numerical analysis, of high accuracy approximate deconvolution regularization models and related algorithms. Analysis of these models and their methods will lead to i) the development of better models with increased accuracy and more efficient algorithms, and ii) discretization strategies and stabilization techniques that will improve stability and accuracy over longer time intervals. The second aspect is the development of an enhanced-physics based scheme for computing solutions to the 3d incompressible Navier-Stokes equations on general domains. By conserving helicity in addition to mass, momentum and energy, long-time accuracy will be achieved through the additional physical fidelity offered by the scheme. To confirm expectations, large-scale long time simulations will be performed on a variety of domains and boundary conditions. The enhanced physics based scheme will be extended to approximate deconvolution models, which are a rare breed of models that conserve energy and helicity in their continuous forms. Additionally, extension of the enhanced-physics based scheme to an energy and potential enstrophy conserving scheme for the shallow water equations will be explored.
The proposed research will lead to more accurate, more physically meaningful, computable approximations to 3d turbulent flow, which in turn will enable long-time accuracy of computed solutions. The need to accurately simulate turbulent fluid flow is paramount for the design of planes, cars, and devices (including medical) that transport fluids. Even for designs where more complex flows need simulated (e.g. multiphase such as in nuclear reactors), the fundamental difficulty is the same as for turbulent flow, and so progress in single phase turbulence is directly relevant. Accuracy over long-time intervals, as well as the portability offered by physics-based models/discretizations, will greatly reduce the need for expensive experimental data and substantially accelerate the design process.
