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A multi-fidelity framework is established and demonstrated for prediction of combustion instabilities in rocket engines. The major idea is to adapt appropriate fidelity modeling approaches for different components in a rocket engine to…
The magnetic Rayleigh-Taylor instability (MRTI) governs plasma mixing and transport in a wide range of astrophysical and laboratory systems. Owing to computational constraints, MRTI is often studied using two-dimensional (2D) simulations,…
Turbulent mixing due to hydrodynamic instabilities occurs in a wide range of science and engineering applications such as supernova explosions and inertial confinement fusion. The experimental, theoretical and numerical studies help us to…
Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…
The motion of unstable fluid interface due to Richtmyer - Meshkov (RM) instability incorporating with density variation has been studied in a spherical target using Lagrangian formulation. During the compression in Inertial Confinement…
A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the…
In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
The compression of a cylindrical gas bubble by an imploding molten lead (Pb) shell may be accompanied by the development of the Richtmyer-Meshkov (RM) instability at the liquid-gas interface due to the initial imperfection of the interface.…
Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and…
A dynamical low-rank approximation is developed for reduced-order modeling (ROM) of the filtered density function (FDF) transport equation, which is utilized for large eddy simulation (LES) of turbulent reacting flows. In this methodology,…
This paper addresses the problem of robust dynamic output stabilization of FO-LTI interval systems with the fractional order 0<{\alpha}<2, in terms of linear matrix inequalities (LMIs). Our purpose is to design a robust dynamic output…
Combustion instabilities are a major concern in the design of Liquid Rocket Engines (LREs) and gas turbines. During this PhD work, several directions were explored to understand and mitigate their effects. First, more efficient and robust…
Mobile manipulator robots operating in complex domestic and industrial environments must effectively coordinate their base and arm motions while avoiding obstacles. While current reactive control methods gracefully achieve this…
This paper deals with designing a robust fixed-order dynamic output feedback controller for uncertain fractional order linear time invariant (FO-LTI) systems by means of linear matrix inequalities (LMIs). Our purpose is to design a low…
Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov…
This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2. A dynamic output feedback controller, with predetermined order, for…
Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…
In the early stages of aerospace design, reduced order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy…
Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the…
This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…