Dept of Aeronautics and Astronautics


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Topics of interest:

Adjoint based error estimation & control:

What is it? When applied to practical flow simulations, CFD solutions inevitably contain numerical error. Adjoint based methods invoke the concept of duality (in addition to the flow solution or the primal problem,  the adjoint approach involves the solution of an appropriately defined dual problem) and can be used to gain an estimate of the numerical error in computing a quantity of interest. More importantly, adjoint methods can also provide  a good indication of where to adapt the mesh to improve accuracy. 

What are we working on? Current research interest is on addressing issues involved  with characterizing the behaviour of continuous and discrete adjoints in flows with strong shocks and investigating the applicability of the adjoint methods to complex problems involving high speed turbulent combustion.

Uncertainty quantification:

What is it? When numerical models are applied in the simulation of complex engineering and physical problems, one would like to have some measure of the confidence that can be placed on the predictive model.  Typically, uncertainties in predictions arise from the physical variability of the system (such as not knowing the right  operating conditions) and also from a lack of knowledge of the system (such as assumptions/errors used in modeling the system). Uncertainty quantiification (UQ) offers a framework that is aimed at propagating these uncertainties through the modeling/simulation chain and essentially provides the user with a quantitative measure of the variability of the desired output (A simplistic way of thinking about it is to imagine assigning error bars to  computational results).

What are we working on? Certain aspects of UQ can be naturally treated in a probabilistic framework. The cost of solving such stochastic problems becomes very expensive when the dimension of the probability space (in other words, the number of uncertain parameters) is large. We are studying the utility of sensitivity and gradient information obtained from the adjoint equations to potentially reduce the cost and improve the accuracy of the UQ analysis. We are also pursuing a novel methodology that uses adjoint equations to simultaneously reduce error in the stochastic and spatial domains. 

Failure modes in Air-breathing Hypersonic Vehicles:

What is involved?  The Aerothermodynamics of an air-breathing scramjet based hypersonic vehicle is a complex multidisciplinary problem involving a variety of modeling challenges including high Mach number external aerodynamics, severe shock-boundary layer interactions, turbulent mixing, combustion, etc.

What are we interested in? We are interested in developing an integrated, uncertainty quantified framework to predict a particulary critical failure mode in such systems called unstart, which results in the disruption of supersonic flow in the engine (and hence, a sudden loss of thrust). Unstart is understood to be instigated by a rise in combustor pressure, unsteadiness, boundary layer separation, thermal loads, etc.  Guided  by a carefully planned experimental campaign (including those that induce unstart under controlled conditions), the various components of the complex system and the fidelity of the relevant modeling tools are studied in detail on sub-system problems and then applied to the full system.

Shock-boundary layer interaction:

What is involved?  Shock-boundary layer interactions occur in many situations of interest in aerospace vehicles undergoing transonic, supersonic or hypersonic flight. When shocks impinge on turbulent boundary layers, the severe adverse pressure gradients can result in flow separation and also affect the pressure recovery downstream of the interaction. Prediction of salient effects can be critical to assessing system performance and reliability.

What are we interested in? In this work, using DNS and LES datasets, we characterize the behavior and accuracy of RANS models. Particular interest is on identifying structural (or model form) uncertainties and possible bounds of RANS solutions.


Future Computing Paradigms


Heterogeneous computers with processors and accelerators are becoming widespread in scientific computing but it is difficult to program hybrid architectures as there is no commonly accepted programming model. Ideally, applications should be written in a way that is portable to many platforms, but providing this portability for general programs is a hard problem. By restricting the class of programs considered, we can make this portability feasible. We are involved with the CS department in the development of a platform called Liszt, a domain specific language for constructing mesh-based PDE solvers that can automatically port programs on to SMP, MPI and GPU platforms.

Wind farms:

We are currently investigating aerodynamic interactions and acoustics from wind farms using highly. accurate numerical schemes.

Stochastic analysis of Wind turbine blade fatigue:

We are exploiting latest advances in uncertainty quantification methods to explore fatigue of blades of large wind turbines.

Improved turbulence and combustion modeling using Machine Learning approaches:


Helicopter blade design:

Time-spectral and adjoint methods are being used to optimize blade shape for improved hover and forward flight performance.





Turbulence in trailing vortices

Subgrid scale closures for the vorticity transport equations

High resolution numerical schemes

Reduced order modeling












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