Codes available:
Data Assimilation
Accurate predictions in Computational Fluid Dynamics (CFD) rely on precise modeling of fluid behavior, yet uncertainties in simulations often limit their reliability. Data Assimilation (DA) helps bridge this gap by combining experimental data with numerical models to refine predictions. However, DA can be computationally expensive, particularly for large-scale applications where high-resolution (HR) simulations demand significant resources. Our research introduces a novel Reduced-Order Model (ROM) that merges experimental data and numerical simulations using DA to enhance CFD predictions. By implementing the Ensemble Kalman Filter (EnKF) within a reduced-dimension framework, we enable accurate state estimation from limited observations while significantly reducing computational costs. Our method applies low-resolution (LR) techniques, including dataset downsampling and advanced reconstruction methods like low-cost Singular Value Decomposition (lcSVD) and Multi-Dimensional Interpolation (MDI), to efficiently restore high-resolution details. The lcSVD approach, never before applied to DA, provides an innovative way to improve accuracy with minimal computational overhead. This strategy demonstrates that the framework is both accurate and computationally efficient, making it suitable for real-time and large-scale fluid dynamics applications. The method will be integrated into the next version of ModelFLOWs-app, enhancing its capabilities for industrial and environmental simulations.
More details about the implementation:
Code in progress. Coming soon…
LcSVD-Data Assimilation
One of the primary challenge associated with the industrial datasets is their heterogeneous nature. The experimental database is normally generated by assimilating the information extracted from a series of sensors placed in the dynamical system. Unlike the sparsely resolved spatial data obtained through experiments we can generate highly resolved spatial information of systems through simulations. These two datasets (experimental and theoretical) independently hold significant information about the combustion system. This mandates the need for a mathematical framework for data assimilation that can simultaneously analyze both datasets by extracting physical information, complementing data, correcting divergent tendencies, and addressing spurious measurements. Low-Cost Singular Value Decomposition (Low-Cost SVD) refers to efficient approximations of the standard SVD algorithm, which reduce computational cost and memory usage while preserving the most important information. These methods are particularly useful for large-scale datasets, high-dimensional data, and real-time applications. In this work low-cost singular value decomposition (lcSVD) is used as a methodology to perform data assimilation.
Code in progress. Coming soon…
Spatio Temporal Koopman Decomposition (STKD)
The Spatio-Temporal Koopman Decomposition (STKD) extends the High-Order Dynamic Mode Decomposition (HODMD) by enabling spatio-temporal analysis of multidimensional data. It represents spatio-temporal fields as combinations of traveling wave modes, each characterized by specific wavenumbers and spatial growth rates, forming intricate standing or propagating patterns. STKD accommodates expansions along multiple spatial dimensions, allowing complex dynamics to be captured across directions such as spanwise and streamwise.In the context of traveling waves, this decomposition allows us to describe how spatial patterns evolve over time in terms of their fundamental modes.STKD analysis helps us understand
a) Dominant Wavenumbers and Frequencies: Identifying which spatial wavenumbers and temporal frequencies dominate the dynamics. b) Growth and Decay: Modes with positive/negative growth rates indicate whether a wave pattern is amplifying or decaying over time.
Download the code here.
The zip file contain all the necessary codes with a tutorial showing its implementation to flow past a 3D cylinder dataset.