Dynamic Systems Commons^™

Bound Preserving Discontinuous Galerkin Methods For Euler Equations And Nonequilibrium Flows, Fangyao Zhu

Dissertations, Master's Theses and Master's Reports

This dissertation is composed of four chapters in which we will closely examine the high order bound preserving discontinuous Galerkin methods for solving partial differential equations, specifically non-equilibrium chemical reacting flows and Euler equations under gravitational fields. A shared requirement between the two is the necessity for positive values of both density and pressure. Due to this physical nature of the two systems, constructing a positivity preserving scheme become very essential in our research.

For non-equilibrium flows where multi-reactions and multi-species are involved, we are also required to keep the bounds of the mass fraction of each species in between …

Data Driven And Machine Learning Based Modeling And Predictive Control Of Combustion At Reactivity Controlled Compression Ignition Engines, Behrouz Khoshbakht Irdmousa

Dissertations, Master's Theses and Master's Reports

Reactivity Controlled Compression Ignition (RCCI) engines operates has capacity to provide higher thermal efficiency, lower particular matter (PM), and lower oxides of nitrogen (NOx) emissions compared to conventional diesel combustion (CDC) operation. Achieving these benefits is difficult since real-time optimal control of RCCI engines is challenging during transient operation. To overcome these challenges, data-driven machine learning based control-oriented models are developed in this study. These models are developed based on Linear Parameter-Varying (LPV) modeling approach and input-output based Kernelized Canonical Correlation Analysis (KCCA) approach. The developed dynamic models are used to predict combustion timing (CA50), indicated mean effective pressure (IMEP), …

Discontinuous Galerkin Methods For Compressible Miscible Displacements And Applications In Reservoir Simulation, Yue Kang

Dissertations, Master's Theses and Master's Reports

This dissertation contains research on discontinuous Galerkin (DG) methods applied to the system of compressible miscible displacements, which is widely adopted to model surfactant flooding in enhanced oil recovery (EOR) techniques. In most scenarios, DG methods can effectively simulate problems in miscible displacements.
However, if the problem setting is complex, the oscillations in the numerical results can be detrimental, with severe overshoots leading to nonphysical numerical approximations. The first way to address this issue is to apply the bound-preserving
technique. Therefore, we adopt a bound-preserving Discontinuous Galerkin method
with a Second-order Implicit Pressure Explicit Concentration (SIPEC) time marching
method to …

Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, Q. Zhong, Demetrios N. Christodoulides, M. Khajavikhan, K. G. Makris, Ramy El-Ganainy

Department of Physics Publications

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time (PT) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other …

Optimization And Control Of An Array Of Wave Energy Converters, Jianyang Lyu

Dissertations, Master's Theses and Master's Reports

This study explored optimal configuration of both the array layout and the dimension of each WEC in the array. The array contains heaving buoys with full interaction and exact hydrodynamics. Optimization of dimension was done on each WEC in the array with a given optimal layout, and a higher q-factor was achieved. Both impedance matching optimal control and derivative control were employed, which provides both theoretical maximum energy and a more realistic case. Then the work was expanded to optimization of both the array layout and the dimension of each WEC in the array. An average of 39.21% higher q-factor …