Current Search: Navon, Ionel Michael (x)
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 Title
 Deterministic and Stochastic Aspects of Data Assimilation.
 Creator

Akella, Santharam, Navon, Ionel Michael, O'Brien, James J., Erlebacher, Gordon, Wang, Qi, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

The principles of optimal control of distributed parameter systems are used to derive a powerful class of numerical methods for solutions of inverse problems, called data assimilation (DA) methods. Using these DA methods one can efficiently estimate the state of a system and its evolution. This information is very crucial for achieving more accurate long term forecasts of complex systems, for instance, the atmosphere. DA methods achieve their goal of optimal estimation via combination of all...
Show moreThe principles of optimal control of distributed parameter systems are used to derive a powerful class of numerical methods for solutions of inverse problems, called data assimilation (DA) methods. Using these DA methods one can efficiently estimate the state of a system and its evolution. This information is very crucial for achieving more accurate long term forecasts of complex systems, for instance, the atmosphere. DA methods achieve their goal of optimal estimation via combination of all available information in the form of measurements of the state of the system and a dynamical model which describes the evolution of the system. In this dissertation work, we study the impact of new nonlinear numerical models on DA. High resolution advection schemes have been developed and studied to model propagation of flows involving sharp fronts and shocks. The impact of high resolution advection schemes in the framework of inverse problem solution/ DA has been studied only in the context of linear models. A detailed study of the impact of various slope limiters and the piecewise parabolic method (PPM) on DA is the subject of this work. In 1D we use a nonlinear viscous Burgers equation and in 2D a global nonlinear shallow water model has been used. The results obtained show that using the various advection schemes consistently improves variational data assimilation (VDA) in the strong constraint form, which does not include model error. However, the cost functional included efficient and physically meaningful construction of the background cost functional term, J_b, using balance and diffusion equation based correlation operators. This was then followed by an indepth study of various approaches to model the systematic component of model error in the framework of a weak constraint VDA. Three simple forms, decreasing, invariant, and exponentially increasing in time forms of evolution of model error were tested. The inclusion of model error provides a substantial reduction in forecasting errors, in particular the exponentially increasing form in conjunction with the piecewise parabolic high resolution advection scheme was found to provide the best results. Results obtained in this work can be used to formulate sophisticated forms of model errors, and could lead to implementation of new VDA methods using numerical weather prediction models which involve high resolution advection schemes such as the van Leer slope limiters and the PPM.
Show less  Date Issued
 2006
 Identifier
 FSU_migr_etd0145
 Format
 Thesis
 Title
 4D Var Data Assimilation and POD Model Reduction Applied to Geophysical Dynamics Models.
 Creator

Chen, Xiao, Navon, Ionel Michael, Sussman, Mark, Hart, Robert, Wang, Xiaoming, Gordon, Erlebacher, Department of Mathematics, Florida State University
 Abstract/Description

Standard spatial discretization schemes for dynamical system (DS), usually lead to largescale, highdimensional, and in general, nonlinear systems of ordinary differential equations.Due to limited computational and storage capabilities, Reduced Order Modeling (ROM) techniques from system and control theory provide an attractive approach to approximate the largescale discretized state equations using lowdimensional models. The objective of 4D variational data assimilation (4D Var) is to...
Show moreStandard spatial discretization schemes for dynamical system (DS), usually lead to largescale, highdimensional, and in general, nonlinear systems of ordinary differential equations.Due to limited computational and storage capabilities, Reduced Order Modeling (ROM) techniques from system and control theory provide an attractive approach to approximate the largescale discretized state equations using lowdimensional models. The objective of 4D variational data assimilation (4D Var) is to obtain the minimum of a cost functional estimating the discrepancy between the model solutions and distributed observations in time and space. A control reduction methodology based on Proper Orthogonal Decomposition (POD), referred to as POD 4D Var, has been widely used for nonlinear systems with tractable computations. However, the appropriate criteria for updating a POD ROM are not yet known in the application to optimal control. This is due to the limited validity of the POD ROM for inverse problems. Therefore, the classical TrustRegion (TR) approach combined with POD (TRPOD) was recently proposed as a way to alleviate the above difficulties. There is a global convergence result for TR, and benefiting from the trustregion philosophy, rigorous convergence results guarantee that the iterates produced by the TRPOD algorithm will converge to the solution of the original optimization problem. In order to reduce the POD basis size and still achieve the global convergence, a method was proposed to incorporate information from the 4D Var system into the ROM procedure by implementing a dual weighted POD (DWPOD) method. The first new contribution in my dissertation consists in studying a new methodology combining the dual weighted snapshots selection and trust region POD adaptivity (DWTRPOD). Another new contribution is to combine the incremental POD 4D Var, balanced truncation techniques and method of snapshots methodology. In the linear DS, this is done by integrating the linear forward model many times using different initial conditions in order to construct an ensemble of snapshots so as to generate the forward POD modes. Then those forward POD modes will serve as the initial conditions for its corresponding adjoint system. We then integrate the adjoint system a large number of times based on different initial conditions generated by the forward POD modes to construct an ensemble of adjoint snapshots. From this ensemble of adjoint snapshots, we can generate an ensemble of socalled adjoint POD modes. Thus we can approximate the controllability Grammian of the adjoint system instead of solving the computationally expensive coupled Lyapunov equations. To sum up, in the incremental POD 4D Var, we can approximate the controllability Grammian by integrating the TLM a number of times and approximate observability Grammian by integrating its adjoint also a number of times. A new idea contributed in this dissertation is to extend the snapshots based POD methodology to the nonlinear system. Furthermore, we modify the classical algorithms in order to save the computations even more significantly. We proposed a novel idea to construct an ensemble of snapshots by integrating the tangent linear model (TLM) only once, based on which we can obtain its TLM POD modes. Then each TLM POD mode will be used as an initial condition to generate a small ensemble of adjoint snapshots and their adjoint POD modes. Finally, we can construct a large ensemble of adjoint POD modes by putting together each small ensemble of adjoint POD modes. To sum up, our idea in a forthcoming study is to test approximations of the controllability Grammian by integrating TLM once and observability Grammian by integrating adjoint model a reduced number of times. Optimal control of a finite element limitedarea shallow water equations model is explored with a view to apply variational data assimilation(VDA) by obtaining the minimum of a functional estimating the discrepancy between the model solutions and distributed observations. In our application, some simplified hypotheses are used, namely the error of the model is neglected, only the initial conditions are considered as the control variables, lateral boundary conditions are periodic and finally the observations are assumed to be distributed in space and time. Derivation of the optimality system including the adjoint state, permits computing the gradient of the cost functional with respect to the initial conditions which are used as control variables in the optimization. Different numerical aspects related to the construction of the adjoint model and verification of its correctness are addressed. The data assimilation setup is tested for various mesh resolutions scenarios and different time steps using a modular computer code. Finally, impact of largescale unconstrained minimization solvers LBFGS is assessed for various lengths of the time windows. We then attempt to obtain a reducedorder model (ROM) of above inverse problem, based on proper orthogonal decomposition(POD), referred to as POD 4D Var. Different approaches of POD implementation of the reduced inverse problem are compared, including a dualweighed method for snapshot selection coupled with a trustregion POD approach. Numerical results obtained point to an improved accuracy in all metrics tested when dualweighing choice of snapshots is combined with POD adaptivity of the trustregion type. Results of adhoc adaptivity of the POD 4D Var turn out to yield less accurate results than trustregion POD when compared with highfidelity model. Finally, we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40yr ECMWF ReAnalysis (ERA40) datasets, in presence of full or incomplete observations being assimilated in a time interval (window of assimilation) presence of background error covariance terms. As an extension of this research, we attempt to obtain a reducedorder model of above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D Var for a finite volume global shallow water equations model based on the LinRood fluxform semiLagrangian semiimplicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dualweighted method for snapshot selection coupled with a trustregion POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4D Var model results combined with the trust region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current research work, we conclude that POD 4D Var certainly warrants further studies, with promising potential for its extension to operational 3D numerical weather prediction models.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd3836
 Format
 Thesis
 Title
 Thermal Conductivity and SelfGeneration of Magnetic Fields in Discontinuous Plasmas.
 Creator

Modica, Frank, Plewa, Tomasz, Navon, Michael Ionel, Sussman, Mark, Department of Scientific Computing, Florida State University
 Abstract/Description

Hydrodynamic instabilities are the driving force behind complex fluid processes that occur from everyday scenarios to the most extreme physical conditions of the universe. The RayleighTaylor instability (RTI) develops when a heavy fluid is accelerated by a light fluid, resulting in sinking spikes, rising bubbles, and material mixing. Laser experiments have observed features of RTI that cannot be explained with pure hydrodynamic models. For this computational study we have implemented and...
Show moreHydrodynamic instabilities are the driving force behind complex fluid processes that occur from everyday scenarios to the most extreme physical conditions of the universe. The RayleighTaylor instability (RTI) develops when a heavy fluid is accelerated by a light fluid, resulting in sinking spikes, rising bubbles, and material mixing. Laser experiments have observed features of RTI that cannot be explained with pure hydrodynamic models. For this computational study we have implemented and verified extended physics mod ules for anisotropic thermal conduction and selfgenerated magnetic fields in the FLASH based Proteus code using the Braginskii plasma theory. We have used this code to simulate RTI in a basic plasma physics context. We obtain results up to 35 nanoseconds (ns) at various resolutions and discuss convergence and computational challenges. We find that magnetic fields as high as 110 megagauss (MG) are genereated near the fluid interface. Thermal conduction turns out to be essentially isotropic in these conditions, but plays the dominant role in the evolution of the system by smearing out smallscale structure and reducing the RT growth rate. This may account for the relatively feature less RT spikes seen in experiments. We do not, however, observe mass extensions in our simulations. Without thermal conductivity, the magnetic field has the effect of generating what appears to be an additional RT mode which results in new structure at later times, when compared to pure hydro models. Additional physics modules and 3D simulations are needed to complete our Braginskii model of RTI.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5841
 Format
 Thesis
 Title
 Adaptive Observations in a 4DVar Framework Applied to the Nonlinear Burgers Equation Model.
 Creator

Hossen, Md. Jakir, Navon, Ionel Michael, Peterson, Janet, Erlebacher, Gordon, Department of Scientific Computing, Florida State University
 Abstract/Description

In 4DVar data assimilation for geophysical models, the goal is to reduce the lack of fit between model and observations (strong constraint approach assuming perfect model). In the last two decades four dimensional variational technique has been extensively used in the numerical weather prediction due to the fact that time distributed observations are assimilated to obtain a better initial condition thus leading to more accurate forecasts using the above 4DVar approach. The use of large...
Show moreIn 4DVar data assimilation for geophysical models, the goal is to reduce the lack of fit between model and observations (strong constraint approach assuming perfect model). In the last two decades four dimensional variational technique has been extensively used in the numerical weather prediction due to the fact that time distributed observations are assimilated to obtain a better initial condition thus leading to more accurate forecasts using the above 4DVar approach. The use of largescale unconstrained minimization routines to minimize a cost functional measuring lack of fit between observations and model forecast requires availability of the gradient of the cost functional with respect to the control variables. Nonlinear Burgers equation model is used as numerical forecast model. First order adjoint model can be used to find the gradient of the cost functional. The use of targeted observations supplementing routine observations contributes to the reduction of the forecast analysis error and can provide improved forecast of weather events of critical societal impact, for instance, hurricanes, tornadoes, sharp fronts etc. The optimal space and time locations of the adaptive observations can be determined by using a singular vector approach. In our work we use both adjoint sensitivity and sensitivity to observation approaches to identify the optimal space and time locations for targeted observations at future time aimed at providing an improved forecast. Both approaches are compared in this work and some conclusions are outlined.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd3765
 Format
 Thesis
 Title
 Development of the Coamps Adjoint Mesoscale Modeling System for Assimilating Microwave Radiances within Hurricanes.
 Creator

Amerault, Clark Mathew, Zou, Xiaolei, Navon, Ionel Michael, O'Brien, James J., Liu, Guosheng, Krishnamurti, T.N., Department of Earth, Ocean and Atmospheric Sciences, Florida...
Show moreAmerault, Clark Mathew, Zou, Xiaolei, Navon, Ionel Michael, O'Brien, James J., Liu, Guosheng, Krishnamurti, T.N., Department of Earth, Ocean and Atmospheric Sciences, Florida State University
Show less  Abstract/Description

An adjoint mesoscale modeling system based on the Naval Research Laboratory's Coupled Ocean Atmosphere Mesoscale Prediction System (COAMPS) atmospheric model was created for use in sensitivity and data assimilation experiments. In addition to the tangent linear and adjoint models of the dynamical core of the COAMPS model, the system includes the tangent linear and adjoint models of the boundary layer turbulent kinetic energy, cumulus, and explicit moist physics parameterizations. The...
Show moreAn adjoint mesoscale modeling system based on the Naval Research Laboratory's Coupled Ocean Atmosphere Mesoscale Prediction System (COAMPS) atmospheric model was created for use in sensitivity and data assimilation experiments. In addition to the tangent linear and adjoint models of the dynamical core of the COAMPS model, the system includes the tangent linear and adjoint models of the boundary layer turbulent kinetic energy, cumulus, and explicit moist physics parameterizations. The inclusion of these adjoint model physics schemes allows for assimilation experiments involving rainaffected observations such as microwave radiances. A radiative transfer model which includes the effects of hydrometeors on atmospheric radiation was linked to the adjoint modeling system to assimilate microwave radiance observations. Probability distribution functions of modelproduced and SSM/I observed brightness temperatures show that the mesoscale prediction overestimates the areas of precipitation, but overall matches the microwave observations quite well. Furthermore, estimates of vertical background error covariance matrices for the hydrometeor variables were calculated using differences between model forecasts which utilized different explicit moisture schemes. The statistics of the differences between the forecasts were assumed to be the same as the statistics of the background error for these variables. The inverse of these matrices (which are needed for data assimilation) were computed using Singular Value Decomposition. Only the largest singular value was kept in calculating the inverse. This ensured that all of the elements of the inverse matrix were nonnegative. Finally, microwave radiance observations for Hurricane Bonnie (1998) were assimilated in a 4dimensional variational data assimilation framework using the COAMPS adjoint model. The modelproduced radiances calculated from the analysis fields after the assimilation process match the observations well for the lower frequency channels which are sensitive to liquid precipitation and water vapor. In the highest frequency channel, where the presence of frozen hydrometeors can have a large impact on the radiance value, the match between the analysis and the observations was not as good. The forecasted hurricane was slightly stronger after the assimilation of microwave radiances in terms of both maximum surface windspeed and minimum central sea level pressure, and some improvement was seen in radiance space as well. More observations from within the hurricane, which will improve the analysis of other variables, will most likely be needed to see a greater forecast impact from the assimilation of these observations.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd0049
 Format
 Thesis
 Title
 Effects of Finite Amplitude Bottom Topography on Ocean Variability.
 Creator

Leonov, Dmitri A., Dewar, William K., Navon, Ionel Michael, Clarke, Allan J., Landing, William M., McWilliams, James C., Nof, Doron, Stern, Melvin E., Department of Earth, Ocean...
Show moreLeonov, Dmitri A., Dewar, William K., Navon, Ionel Michael, Clarke, Allan J., Landing, William M., McWilliams, James C., Nof, Doron, Stern, Melvin E., Department of Earth, Ocean and Atmospheric Sciences, Florida State University
Show less  Abstract/Description

The winddriven oceanic circulation in the presence of bottom topography that isopycnals intersect is examined in an idealized setting. A modified quasigeostrophic (QG) model has been designed and implemented. The model allows staircase bottom topography: topographic breaks decompose the lateral domain into subdomains consisting of fixed numbers of layers. Topographic shelves are placed within small (order Rossby number) vertical distances from the undisturbed layer interfaces. Each shelf...
Show moreThe winddriven oceanic circulation in the presence of bottom topography that isopycnals intersect is examined in an idealized setting. A modified quasigeostrophic (QG) model has been designed and implemented. The model allows staircase bottom topography: topographic breaks decompose the lateral domain into subdomains consisting of fixed numbers of layers. Topographic shelves are placed within small (order Rossby number) vertical distances from the undisturbed layer interfaces. Each shelf can have topographic variations of the same scale. An elliptic solver inverting potential vorticity into geostrophic stream functions was designed based on the Capacitance matrix method. Solutions are matched at the topographic breaks by adding fictitious potential vorticity sources. The model has been tested against the problem of trapped topographic waves over a cliff. The results obtained for smallsteepness disturbances agree with a weakly nonlinear theory developed by Dewar and Leonov. Steeper disturbances break in a way that favors on shelf eddy detachment and transport of undiluted properties onto the shelf. The model has been further applied to the basinscale winddriven circulation problem in a 3layer configuration with a continental shelf in the western part of the domain. Doublegyre wind forcing has been considered. The topographic shelves are responsible for dynamics absent in classical idealized eddy resolving QG models which have been the preferred numerical tool for the study of low frequency intrinsic ocean variability. The toplayer flow interacts with the shelf topography by means of vortex tube stretching and vorticity dissipation due to bottom drag. This mechanism reduces the role of horizontal friction as a controlling factor in the dynamics.The results obtained for different parameter regimes (freeslip, noslip boundary condition, different values of the viscosity) show reduced sensitivity to the type of dynamic boundary condition, compared to classical results. The intrinsic variability of the flow is affected by the new mechanism of on and off shelf transport of potential vorticity. The role of horizontal friction is again reduced, as shown by the modeling results. Spatiotemporal patterns of the variability have been analyzed. Most of the patterns are insensitive to the type of boundary condition (freeslip vs. noslip), and qualitatively resemble classical noslip results.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd3121
 Format
 Thesis
 Title
 Practical Optimization Algorithms in the Data Assimilation of LargeScale Systems with NonLinear and NonSmooth Observation Operators.
 Creator

Steward, Jeffrey L. (Jeffrey Lawrence), Navon, Ionel Michael, Liu, Guosheng, Gunzburger, Max, Erlebacher, Gordon, Zupanski, Milijia, Karmitsa, Napsu, Department of Scientific...
Show moreSteward, Jeffrey L. (Jeffrey Lawrence), Navon, Ionel Michael, Liu, Guosheng, Gunzburger, Max, Erlebacher, Gordon, Zupanski, Milijia, Karmitsa, Napsu, Department of Scientific Computing, Florida State University
Show less  Abstract/Description

This dissertation compares and contrasts largescale optimization algorithms in the use of variational and sequential data assimilation on two novel problems chosen to highlight the challenges in nonlinear and nonsmooth data assimilation. The first problem explores the impact of a highly nonlinear observation operator and highlights the importance of background information on the data assimilation problem. The second problem tackles largescale data assimilation with a nonsmooth...
Show moreThis dissertation compares and contrasts largescale optimization algorithms in the use of variational and sequential data assimilation on two novel problems chosen to highlight the challenges in nonlinear and nonsmooth data assimilation. The first problem explores the impact of a highly nonlinear observation operator and highlights the importance of background information on the data assimilation problem. The second problem tackles largescale data assimilation with a nonsmooth observation operator. Together, these two cases show both the importance of choosing an appropriate data assimilation method and, when a variational or variationallyinspired method is chosen, the importance of choosing the right optimization algorithm for the problem at hand.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5203
 Format
 Thesis
 Title
 I. A Modified ƙƐ Turbulence Model for High Speed Hets at Elevated Temperatures. II. Modeling and a Computational Study of Spliced Acoustic Liners.
 Creator

Ganesan, Anand, Tam, Christopher K. W., Nh, HonKie, Hunter, Christopher, Navon, Ionel Michael, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

A modification to the kepsilon model aimed to extend its applicability to the computation of the mean flow and noise of highspeed hot jets is proposed. The motivation of the proposal arises from the observation that there is a large density induced increase in the growth rate of spatial instabilities of a mixing layer if the lighter fluid moves faster. This consideration leads to the incorporation of a density gradient related contribution to the turbulent eddy viscosity of the kepsilon...
Show moreA modification to the kepsilon model aimed to extend its applicability to the computation of the mean flow and noise of highspeed hot jets is proposed. The motivation of the proposal arises from the observation that there is a large density induced increase in the growth rate of spatial instabilities of a mixing layer if the lighter fluid moves faster. This consideration leads to the incorporation of a density gradient related contribution to the turbulent eddy viscosity of the kepsilon model. Computed jet mean flow profiles and centerline velocity distributions at elevated temperatures of highspeed jets are found to be in better agreement with experimental measurements if density modification is included. Noise predictions including density effect are also found to be in better agreement with microphone measurements. The good agreements offer strong support to the validity and usefulness of the proposed density correction formula. A timedomain computational methodology has been deveoped to study the propagation and acoustic scattering of fan tones by spliced liners. The front portion of the engine is modelled as a duct. Significant acoustic scattering is observed for a frequency pretty close to cutoff. In this case, total scattered energy was found to be more than the energy in the incident mode. The spliced liners, in such conditions, are found to be less effective than the uniform liners. The performance of the liner was found to be dependent on the frequency. The results of the simulations agree qualitiatively well with the available experimental and theoretical work.
Show less  Date Issued
 2005
 Identifier
 FSU_migr_etd4368
 Format
 Thesis
 Title
 Calibration of Local Volatility Models and Proper Orthogonal Decomposition Reduced Order Modeling for Stochastic Volatility Models.
 Creator

Geng, Jian, Navon, Ionel Michael, Case, Bettye Anne, Contreras, Rob, Okten, Giray, Kercheval, Alec N., Ewald, Brian, Department of Mathematics, Florida State University
 Abstract/Description

There are two themes in this thesis: local volatility models and their calibration, and Proper Orthogonal Decomposition (POD) reduced order modeling with application in stochastic volatility models, which has a potential in the calibration of stochastic volatility models. In the first part of this thesis (chapters IIIII), the local volatility models are introduced first and then calibrated for European options across all strikes and maturities of the same underlying. There is no...
Show moreThere are two themes in this thesis: local volatility models and their calibration, and Proper Orthogonal Decomposition (POD) reduced order modeling with application in stochastic volatility models, which has a potential in the calibration of stochastic volatility models. In the first part of this thesis (chapters IIIII), the local volatility models are introduced first and then calibrated for European options across all strikes and maturities of the same underlying. There is no interpolation or extrapolation of either the option prices or the volatility surface. We do not make any assumption regarding the shape of the volatility surface except to assume that it is smooth. Due to the smoothness assumption, we apply a second order Tikhonov regularization. We choose the Tikhonov regularization parameter as one of the singular values of the Jacobian matrix of the Dupire model. Finally we perform extensive numerical tests to assess and verify the aforementioned techniques for both local volatility models with known analytical solutions of European option prices and real market option data. In the second part of this thesis (chapters IVV), stochastic volatility models, POD reduced order modeling are introduced first respectively. Then POD reduced order modeling is applied to the Heston stochastic volatility model for the pricing of European options. Finally, chapter VI summaries the thesis and points out future research areas.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7388
 Format
 Thesis
 Title
 Characterization of Coherent Structures in QuasiSteady State Astrophysical Fluid Flows.
 Creator

Learn, Ryan Joseph, Plewa, Tomasz, Ye, Ming, Erlebacher, Gordon, Navon, Ionel Michael, Florida State University, College of Arts and Sciences, Department of Scientific Computing
 Abstract/Description

In astrophysical hydrodynamical objects, multiple physical processes take place on a wide variety of spatial and temporal scales simultaneously, making direct numerical simulation of such objects dicult computationally. Our work focuses on developing and testing reducedorder models of such physical processes and objects in order to mitigate this diculty. We use the singular value decomposition on snapshot data the systems generated by a highdelity model in order to generate a singular...
Show moreIn astrophysical hydrodynamical objects, multiple physical processes take place on a wide variety of spatial and temporal scales simultaneously, making direct numerical simulation of such objects dicult computationally. Our work focuses on developing and testing reducedorder models of such physical processes and objects in order to mitigate this diculty. We use the singular value decomposition on snapshot data the systems generated by a highdelity model in order to generate a singular eigenvalue spectrum as well as a orthogonal eigenfunction basis. The original equations of the system are then projected onto this basis via a Galerkin or discontinuous Galerkin projection, giving rise to a system of ordinary dierential equations that serve as the reduced order model. These models are then propagated forward in time, and their accuracy and computational cost are compared with our highdelity models. We nd that for the systems of interest (quasisteady systems), high accuracy reduced order models can be created with only a small number of basis functions at a cost of an order of magnitude less computational time. We further propose methods to increase the savings for these systems even further.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9637
 Format
 Thesis