Advanced Data Assimilation

High-fidelity Simulations in the era of data

Scalar source reconstruction in turbulent environments

Olfactory search in canonical turbulent setups

The difficulty of reconstruction lies in the highly-correlated sensor measurements when the source is shifted. The effect of turbulent dispersion and molecular diffusion onto the quality of the reconstruction is investigated and reported. This project is currently funded by NSF.

Optimal sensor placement

We developped a formulation to minimize the condition number of the source-search problem. The left panel in the example shows the computational domain. The right panel shows the condition number for different sensor locations. The optimal sensor is located at the edge of the scalar plume, where the ability to differentiate measurements from is significantly improved.

Data assimilation in turbulent flows

Domain of dependence for measurements in compressible and incompressible flows

The iso-surface of adjoint variables starting from different measurement kernels at the wall. These adjoint structures represent the domain of dependence for the measurement.

Figure: Side views of the u-velocity contour from the true (a),observation-interpolated (b), and reconstructed (c) fields, respectively. Available velocity observations are marked by small spheres. Particles closer to the plane are marked with larger sizes

Hierarchical Adjoint-based DA with PIV measurements

We plan to take multi-fidelity models to perform data assimilation and enhance the efficiency and applicability. This project has been funded by NSF.

CNN-based auto encoder
for turbulent channel flow

A combined effort to perform data assimilation with nonlinear reduce-order models.

ODI-aided data assimilation in turbulent flows

The novelty of this work consists of implementing the Parallel-Ray Omnidirectional Integration method into an in-housed developed Navier-Stokes solver to compute the pressure. The omnidirectional integration method is known to give better performances in reconstructing the pressure field from error-embedded pressure gradient measurements in comparison with conventional pressure Poisson solvers with Neumann Boundary condition.

Data Assimilation in an Eulerian-Lagrangian framework

Particle Forcing Reconstruction

When measurements regarding particle locations are available but sparse, directly evaluation of the forcing is intractable. Nevertheless, the forcing for finite-size particles is determined using adjoint-based data assimilation. This inverse problem is formulated within the framework of optimization, where the cost function is defined as the difference between the measured and predicted particle locations. The gradient of the cost function, with respect to the forcing can be calculated from the adjoint dynamics. Funded by AFOSR.

Data assimilation with noisy data using probablistic methods

Gaussian Process Regression for
pressure reconstruction

Many numerical algorithms have been established to reconstruct pressure fields from measured kinematic data with noise by Particle Image Velocimetry (PIV), such as the Pressure Poisson solver and the Omni-Directional Integration (ODI) method. This study adopts Gaussian Process Regression (GPR), a probabilistic framework with an intrinsic de-noising mechanism to tackle drawbacks of traditional Pressure Poisson solver and compares the performance with ODI.

Physics-constrained generative model for inverse problem

Diffusion model for reverse physics

A recent funded project by NSF

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