Accurate Prediction of Fluid Motion

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

Accurate prediction of fluid motion and materials thereby transported is essential for many critical engineering and scientific applications. As two examples, flow predictions are key to limiting damage of hurricanes to human life and to the economy (the latter estimated to be hundreds of billions of dollars in 2017) and to energy efficiency optimization (85% of US energy is generated by combustion for which accurate simulation of turbulent mixing is critical). Unfortunately, fundamental barriers to accurate, efficient and reliable prediction of fluid flow exist in these and other applications addressed in the proposed research. Accurate prediction with uncertain data requires reliable and efficient ensemble simulations. The cost of current methods limits prediction accuracy by limiting ensemble sizes. Further improvement requires new computational tools with a fundamental decrease in simulation cost and memory requirements. Algorithms which address these needs will be developed in this project. Artificial compression methods are by far the most efficient per time step but little used due to low time accuracy, restrictive time step conditions, stability problems, ill-conditioning and nonphysical acoustic waves. Their resolution will resurrect artificial compression methods into accurate, reliable and efficient methods for the prediction of fluid motion, expanding ensemble simulations and coupled flow prediction markedly beyond their current limitations. Artificial compression methods exhibit parasitic pressure waves that become resonant at higher Reynolds numbers. This research will develop a method dependent Lighthill theory of flow generated sound and apply it to design time filters to suppress parasitic acoustics. Time accuracy will be achieved by development of a new family of variable step, variable order methods. Variable step, variable order method have proven to be the most efficient, accurate and reliable methods to solve smaller systems of ordinary differential equations. However, previous variable step, variable order methods have limited penetration into computational fluid dynamics practice due partially to their implementation complexity and increased cost per step. The new methods have (to leading order) the same cognitive and computational complexity as the fully implicit method. Uncoupling of velocity and pressure in artificial compression methods introduces an extra grad-div term in the velocity solve, decreasing sparsity and increasing ill conditioning. Thus, the efficiency of artificial compression methods is lost with increased storage and solver cost per step. The research will develop a new realization, modular Grad-Div, reducing storage and turnaround time by a factor of 30 in preliminary tests. While each development has independent interest, they will be integrated into an ensemble, artificial compression method and tested on problems of compelling interest. The proposed research develops expertise of PhD students in analysis, numerical analysis and application areas while working on compelling mathematics problems of broad impact advancing the accurate prediction of fluid motion. It is carefully integrated with the development of the PI's PhD students and undergraduate researchers. Within the project, each PhD student can develop their own research agenda and collaborate at the points of contact among the research problems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.