Our research involves the development of computational algorithms and models with application to fluid flows. This includes fluid dynamic modeling at a fundamental level as well as in an integrated system-level setting. An overarching theme in our lab involves the use of simulation and data-driven methods to answer scientific and engineering questions with an appreciation of the effect of numerical errors and modeling uncertainties on the predicted results.
Read more about our work in these two websites:
Data-driven modeling for scientific computing
We have developed a new paradigm that combines field inversion and machine learning to enable data-driven modeling. Our critical contribution is the idea that spatio-temporal discrepancies (which are determined by inverse modeling) can be transformed into functional forms that can be embedded into a predictive model. A bare-bones schematic can be found here . This is a long term effort and we are methodically exploring many aspects of the process including generating the data via design of experiments, developing/extending machine learning methods as well as addressing computer science aspects. These activities have directly led to the establishment of the Center for Data-driven Computational Physics . While these ideas are general, application to turbulence modeling is is being coordinated in in a collaborative project. .
Funded by NASA and NSF/MRI .
This research seeks to develop a new generation of turbulence models for use in engineering predictions. This encompasses
(i) Theoretical approach: A unique approach that describes the state of turbulence using the morphology of coherent structures, and
(ii) Data-driven approach: Aided by inversion and machine learning models.
(iii) 'Mathematical approach': Aided by the mathematics of the coarse-graining process (using projection operator-type ideas).
Funded by NASA, NSF/CDESE and AFOSR .
Novel techniques for statistical coarse graining
We are developing mathematically-consistent models using ideas from statistical mechanics that account for the impact of unresolved physics and numerical errors on resolved variables. The novelty is that time-history (non-Markovian) effects which have long been ignored in traditional large eddy simulation approaches can be formally represented. The techniques developed in this effort have applicability in a wide range of problems.
Funded by AFOSR .
Adaptive control using data-based techniques
We seek to extend data-driven adaptive control to systems that are beyond the capability of traditional adaptive control algorithms due to the extreme complexity of the physics. This will be accomplished by developing, demonstrating, and validating a novel diagnostic modeling methodology that that is based on limited sensor data to uncover the essential dynamics of the system. Specificially, we combine multidisciplinary expertise in adaptive control and system identification; computational fluid dynamics and data-driven modeling; and combustion dynamics and physics-guided diagnostics. The venue for developing, demonstrating, and validating the proposed diagnostic modeling methodology is experimental control of instability in lean premixed combustion.
Funded by NSF/CMMI .
This research addresses the fundamental question: In the process of making computational predictions, how best can we affix “error-bars” on simulation outputs? The ultimate goal is to develop a unified framework that not only accounts for randomness and variability in the system of interest, but also to quantitatively express our deficiencies in modeling the system. We are using adjoint techniques extensively to address discretization and sampling errors and field inference and machine learning to address model form errors. Under DARPA funding, we are embedding this approach within a Design Under Uncertainty (DUU) setting. The immediate application is aerothermal/structural design of a fighter aircraft nozzle.
Funded by DARPA .
Efficient numerical schemes for the vorticity transport equations
With a view towards computing high Reynolds number vortex dominated flows such as those in the wakes of helicopters and ships, we are developing techniques to solving fluid flow equations in vorticity-velocity form. This technique presents inherent advantages over solving the conventional Navier—Stokes equations because coherent structures can be compactly described in terms of Vorticity variables. Toward this end, we are developing sharp gradient-capturing numerical schemes such coherent structures can be resolved using a relatively small number of mesh points over the length scales.
Funded by Continuum Dynamics, Inc. and Navy .
Reduced Order Modeling
We are exploring techniques to reduce the dimensionality of large-scale complex systems. We are developing techniques to parameterize the impact of unresolved scales on the resolved variables and exploring techniques that can significantly promote sparse approximations.
Liquid-fueled Rocket engines
The main objective is to enable efficient and accurate predictions of combustion dynamics in practical liquid rocket engines (LREs). Towards this end, we seek to develop and demonstrate mathematically-derived reduced order models (ROMs) as well as physically-inspired reduced fidelity models (RFMs). LREs involve extreme complexities, primarily due to the presence of a large number of injectors and the associated flow/combustion interactions. To address the goal of full-system predictions, we will assemble a multi-fidelity simulation tool composed of ROMs and RFMs. Our framework will transform simulation data and expert knowledge into a computationally efficient reduced description of the full-scale physics. These models will be trained using a physics-constrained data-driven approach that operates on an organized hierarchy of simulations.
Unmanned Air Vehicles (UAVs)
We are developing techniques to a) characterize realistic operating environments of UAVs and b) develop an accuracte flight dynamic model with the goal of planning optimal trajectories.
Funded by NASA .
Helicopter-ship board dynamics interface
We are developing surrogate and reduced order techniques to efficiently simulate the operation of helicopters in the airwakes of ships.
Funded by Navy .
With the on-going emphasis on fuel economy, reducing aerodynamic drag in road vehicles is a critical concern for the automotive industry. We have begun work to build a platform which can be used to rapidly study the impact of shape modifications on the aerodynamic performance, by exploring parametric shape modifications. Another target is the integration of wind tunnel results with the computational models such that both techniques can be used in design.
Funded by General Motors .
High-speed air vehicles
We are extending our science and solvers, to unit (shock-boundary layer interactions, etc), and system level (scramjet flow path, etc) applications pertaining to high-speed aircraft.
Personal aircraft, powered by batteries have the potential to re-invigorate aviation. We are using our suite of computational tools to analyze and design distributed propulsion systems. Specifically, we are studying efficient propeller designs for improved performance and noise as well as optimal wing designs to beneficially utilize the propeller wake.
We are exploring the performance limits and design of unconventional concepts in wind energy. These include vertical axis wind turbine farms, shrouded wind turbines, etc.
Please read the requirements for this position here.
The applicant is expected to have leading expertise in at least one of the following areas:
We are looking for one or more post-doctoral researchers.
The applicant is expected to have a strong background in at least one of the following areas: