Siva Viknesh

Siva Viknesh

Ph.D. in Mechanical Engineering

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Grid sensitivity and role of error in computing a lid-driven cavity problem

Published in Physical Review E, 2019

This study investigates grid sensitivity in the bifurcation problem of lid-driven cavity (LDC) flow using very fine grids. Researchers have reported different critical Reynolds numbers (Recr1) for the first bifurcation, influenced by formulation, numerical methods, and grid selection. Using a highly accurate parallel algorithm, results were obtained on fine grids (1025×1025 and 2049×2049), providing insights into the computational physics of LDC flow. The findings highlight the interchangeable roles of numerical errors and real-flow disturbances, stressing the need for explicit excitation in compact schemes. These results offer universal benchmarks for solving the Navier-Stokes equation for LDC with near-spectral accuracy.

Recommended citation: Suman, V. K., Viknesh S., Siva, Tekriwal, M. K., Bhaumik, S., & Sengupta, T. K. (2019). "Grid sensitivity and role of error in computing a lid-driven cavity problem." Phys. Rev. E, 99(1), 013305.
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Active control of separated flow on a symmetric airfoil by pitching oscillation

Published in Physics of Fluids, 2021

This research investigates the control of massively separated flow over a symmetric airfoil through low-amplitude pitching oscillations. Two airfoils with different thickness-to-chord ratios are analyzed to examine the effects of thickness and stall type on flow control. Aerodynamic forces and moments are computed using surface and wake pressure data, while time-resolved particle image velocimetry and unsteady pressure measurements characterize the flow field. The study provides insights into the dynamic response of a stalled airfoil to varying oscillation frequencies and proposes an optimal pitching frequency for enhanced flow control. Additionally, a data-driven aerodynamic model based on Fourier analysis is developed for airfoils in the post-stall regime.

Recommended citation: Siva Viknesh, S., & Poddar, K. (2021). "Active control of separated flow on a symmetric airfoil by pitching oscillation." Physics of Fluids, 33(8), 087115.
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AI-augmented hemodynamics: 3D blood flow field construction from pressure measurements

Published in APS - Divison of Fluid Dynamics, 2023

This paper introduces a deep learning method using physics-informed neural networks (PINN) to create a 3D blood flow velocity field from pressure data measured along the centerline of an artery, specifically using instantaneous wave-free ratio (iFR) measurements. The approach leverages recent advancements in PINN, including neuron-wise adaptive activation functions, to effectively solve complex 3D flow fields in stenosed arteries. The paper also addresses the causality issues inherent in the PINN framework across spatial domains and proposes a solution to determine unknown inlet and outlet boundary conditions, enabling the calculation of the entire flow field from pressure data. The framework is applied to a patient-specific coronary artery stenosis model, demonstrating its accuracy and the potential to obtain comprehensive blood flow field data from experimental pressure wire measurements.

Recommended citation: Viknesh, S., Shoemaker, E., Arzani, A. (2023). " AI-augmented hemodynamics: 3D blood flow field construction from pressure measurements." APS-DFD Conference.
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Role of flow topology in wind-driven wildfire propagation

Published in Submitted, 2024

This study investigates wildfire propagation by analyzing the interaction between wind velocity, fuel, and terrain. A revised non-dimensionalization of the combustion model introduces two new non-dimensional numbers, aiding in the prediction of wildfire spread. A state-neutral curve was derived to identify conditions for wildfire extinction. A wildfire transport solver using advanced numerical methods models the influence of wind topology, examining both steady and unsteady wind conditions. The wildfire's response to varying wind oscillation frequencies is assessed, with comparisons to Lagrangian coherent structures (LCS). These findings offer improved insights for wildfire modeling and management strategies.

Recommended citation: Viknesh, S., Tohidi, A., Afghah, F., Stoll, R., Arzani, A. (2024) 'Role of flow topology in wind-driven wildfire propagation'
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ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identification

Published in Submitted, 2024

Traditional methods like Sparse Identification of Nonlinear Dynamics (SINDy) and symbolic regression have notable limitations in extracting governing equations from observational data. To address these, we introduce ADAM-SINDy, a novel methodology within the SINDy framework that incorporates the ADAM optimization algorithm. This approach enables simultaneous optimization of nonlinear parameters and coefficients without prior knowledge of characteristics such as trigonometric frequencies or polynomial exponents. ADAM-SINDy dynamically adjusts unknown variables based on system-specific data, enhancing the identification process and reducing sensitivity to the candidate function library. Demonstrated across various dynamical systems, including coupled nonlinear ordinary differential equations and wildfire transport models, our results show significant improvements in parameter identification.

Recommended citation: Viknesh, S., Tatari, Y., Arzani, A. (2024). "ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identification"
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Flow topology and wind-driven wildfire propagation

Published in APS - Divison of Fluid Dynamics, 2024

This work examines the impact of wind flow patterns on wildfire propagation by revisiting the Asensio wildfire model and introducing a non-dimensionalization that considers three distinct time scales, resulting in two non-dimensional numbers. A scaling analysis is conducted to analyze wildfire behavior under these numbers. A wildfire transport solver is developed using a finite difference method with compact spatial schemes and an implicit-explicit Runge-Kutta integrator. The study investigates transient wildfire behavior under steady wind velocity, focusing on saddle-type fixed points and the role of the non-dimensional numbers. It also explores unsteady wind conditions through double gyre flow, analyzing different oscillation frequencies and amplitudes. The findings underscore the complex interactions between wildfire dynamics and wind patterns, enhancing understanding of wind-driven wildfire behavior.

Recommended citation: Viknesh, S. Tohidi, A., Afghah, F., Stoll, R., Arzani, A. (2024). " Flow topology and wind-driven wildfire propagation." APS-DFD Conference.
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SGD-SINDy: Stochastic Gradient-Descent based Framework for Flexible System Identification

Published in APS - Divison of Fluid Dynamics, 2024

We introduce a novel methodology within the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, called SGD-SINDy, which utilizes stochastic gradient descent (SGD) optimization to improve parameter identification while reducing reliance on predefined candidate libraries. Unlike traditional SINDy, SGD-SINDy efficiently identifies parameters without prior knowledge of linear distributions or nonlinear characteristics such as frequencies and bandwidths. It also streamlines hyperparameter tuning by optimizing them concurrently during the process. Our approach demonstrates significant effectiveness across various dynamical systems, including harmonic oscillators, Van der Pol oscillators, chaotic ABC flow, and reaction kinetics, showcasing substantial improvements in parameter identification, particularly in nonlinear contexts. This highlights the potential of SGD optimization to advance SINDy-based analyses.

Recommended citation: Arzani, A., Viknesh, S., Tatari, Y. (2024). " SGD-SINDy: Stochastic Gradient-Descent based Framework for Flexible System Identification." APS-DFD Conference.
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