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
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
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
(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
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
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.
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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