Search Results (1 - 14 of 14 Results)

Sort By  
Sort Dir
 
Results per page  

Kung, Christopher W.Development of a Time Domain Hybrid Finite Difference/Finite Element Method For Solutions to Maxwell’s Equations in Anisotropic Media
Doctor of Philosophy, The Ohio State University, 2009, Electrical and Computer Engineering

The finite difference time domain (FDTD) and finite element numerical methods are two popular time domain computational methods in electromagnetics, but the two numerical methods have certain tradeoffs. FDTD is a fast explicit method with second order accuracy, but the method’s accuracy is reduced when analyzing structures that are not conforming to a Cartesian grid. The finite element method on the other hand excels at examining domains with non-conforming structures, but its method of solution usually requires a matrix inverse operation, which is computationally expensive. Fortunately, research in hybrid methods have shown that the FDTD method for isotropic materials can be viewed upon as a subset of finite elements, and from this viewpoint, the FDTD and finite element method in the time domain can be hybridized together to the advantages of both methods while mitigating the disadvantages.

With the recent rise in the study of metamaterials, which contain anisotropic media, having a hybridized method to study anisotropic media is a desirable tool as, for example, the effects of these materials combined with antennas are being examined. However, the hybridization approach combining the FDTD and finite element method for isotropic media does not extend to anisotropic media since the anisotropic FDTD equation cannot be recovered from the finite element formulation in this fashion. In this dissertation, a hybridized FDTD/finite element method for anisotropic materials will be developed. In the derivation of the hybridized method, a new finite element method will be formulated which incorporates the constitutive relation in a finite element point of view. This new finite element method will also be used to construct new anisotropic FDTD stencils in a systematic manner for certain interface and boundary conditions that the traditional anisotropic FDTD update fails to handle. Numerical tests will be performed to demonstrate the accuracy of the both the hybridized anisotropic FDTD/finite element method as well as the new FDTD stencils that are derived from the new finite element method.

Committee:

Robert Lee, PhD (Advisor); Fernando Teixeira, PhD (Committee Member); Prabhakar H. Pathak, PhD (Committee Member)

Subjects:

Electrical Engineering; Electromagnetism

Keywords:

finite difference; finite element; anisotropic materials; hybrid numerical methods; time domain; electromagnetics

POONDRU, SHIRDISHA NEW DIRECT MATRIX INVERSION METHOD FOR ECONOMICAL AND MEMORY EFFICIENT NUMERICAL SOLUTIONS
MS, University of Cincinnati, 2003, Engineering : Mechanical Engineering
The past decade has witnessed a great deal of progress in the area of computational fluid dynamics (CFD). Developments in computer technology hardware as well as in advanced numerical algorithms have made CFD a very important tool for attacking the complex problems in fluid mechanics and heat transfer which are governed by partial differential equations (PDEs). Though the cost of computer memory has been decreasing rapidly, memory can still be a limiting factor and so the quest for more economical and memory efficient methods continues till date. In this thesis we introduce and examine in detail the new Direct Matrix Inversion (DMI) method to solve some model PDEs. These model equations include the heat equation and Laplace’s equation. The present method inverts the tri-diagonal or penta-diagonal coefficient matrices, representing the finite difference approximation of model equations directly in the symbolic form, which was considered impractical previously. Moreover, the inverse of the coefficient matrix requires storage space for very few elements and the majority of elements of the inverse matrix are then calculated using recursive formulas, thereby making the method very economical. In addition, for unsteady equations the coefficients of the inverse matrix are obtained in symbolic form just once and then used in the numerical solutions at different time levels. The present method has advantages in terms of memory requirement, accuracy and robustness. Numerical results for the two-dimensional incompressible Navier-Stokes equations are obtained to demonstrate the robustness and efficiency of the present method using the flow in a driven square cavity as the model problem. The computed results validate the analytical development of our new method.

Committee:

Dr. Shaaban A. Abdallah (Advisor)

Subjects:

Engineering, Mechanical

Keywords:

numerical methods; direct matrix inversion; memory efficient methods

Mullenix, Nathan JA COUPLED GAS DYNAMICS AND HEAT TRANSFER METHOD FOR SIMULATING THE LASER ABLATION PROCESS OF CARBON NANOTUBE PRODUCTION
Master of Science, University of Akron, 2005, Mechanical Engineering
Laser ablation is a complex process that involves the heating of a target material, the phase change of a portion of that material, and the subsequent expansion of the removed material. In the particular case of carbon nanotube production, the quality and quantity of the nanotubes depends greatly on the properties of the expanding plume of material. Current models of this process do not take into account the coupling of the behavior of the ablated plume and the thermal processes occurring within the target. A physic model is developed that takes into account this coupling. The heat transfer within the target is modeled as conduction with surface absorption of the laser. The material removal process is considered to be sublimation governed by the Hertz-Knudsen equation or a method based on the latent enthalpy of sublimation. The gas dynamics are modeled using both the 1-D and 2-D axisymmetric Euler equations. Numerical methods are then implemented to simulate this physical model. The independent numerical models are tested against standard test cases. These numerical models are then implemented in a stongly coupled framework. The provided results are compared to available literature. Comparisons are made between the two sublimation models, and the two gas-dynamics models. Future work required to improve the model is discussed

Committee:

Alex Povitsky (Advisor)

Subjects:

Engineering, Mechanical

Keywords:

Laser Ablation; Carbon Nanotubes; Hertz-Knudsen Equation; Sublimation; Strongly-Coupled Ablation; Numerical Methods

GRANT, IVANFLOW INDUCED VIBRATIONS IN PIPES, A FINITE ELEMENT APPROACH
Master of Science in Mechanical Engineering, Cleveland State University, 2010, Fenn College of Engineering
Flow induced vibrations of pipes with internal fluid flow is studied in this work. Finite Element Analysis methodology is used to determine the critical fluid velocity that induces the threshold of pipe instability. The partial differential equation of motion governing the lateral vibrations of the pipe is employed to develop the stiffness and inertia matrices corresponding to two of the terms of the equations of motion. The equation of motion further includes a mixed-derivative term that was treated as a source for a dissipative function. The corresponding matrix with this dissipative function was developed and recognized as the potentially destabilizing factor for the lateral vibrations of the fluid carrying pipe. Two types of boundary conditions, namely simply-supported and cantilevered were considered for the pipe. The appropriate mass, stiffness, and dissipative matrices were developed at an elemental level for the fluid carrying pipe. These matrices were then assembled to form the overall mass, stiffness, and dissipative matrices of the entire system. Employing the finite element model developed in this work two series of parametric studies were conducted. First, a pipe with a constant wall thickness of 1 mm was analyzed. Then, the parametric studies were extended to a pipe with variable wall thickness. In this case, the wall thickness of the pipe was modeled to taper down from 2.54 mm to 0.01 mm. This study shows that the critical velocity of a pipe carrying fluid can be increased by a factor of six as the result of tapering the wall thickness.

Committee:

Majid Rashidi, PhD (Committee Chair); Rama S Gorla, PhD (Committee Member); Asuquo B Ebiana, PhD (Committee Member)

Subjects:

Design; Fluid Dynamics; Mechanical Engineering

Keywords:

finite element analysis; Flow induced vibrations; Matlab programming ; numerical methods; flow through pipes

Chalas, Jeffrey MichaelDesign and Location Optimization of Electrically Small Antennas Using Modal Techniques
Doctor of Philosophy, The Ohio State University, 2015, Electrical and Computer Engineering
In this dissertation, the Theory of Characteristic Modes is used as a framework for the design, optimization, and benchmarking of electrically small radiating systems. The foundation of this work is in the theory of Characteristic Modes, an eigenvalue equation of the Method of Moments impedance matrix [Z], that leads to derive the fundamental radiation modes of arbitrary-shaped bodies. After an overview of small antenna theory, we derive a new method for computing the Q factor of arbitrary-shaped radiating bodies using CMs using only the Method of Moments impedance matrix [Z]. Following this derivation, we present a new method for computing the fundamental limits on Q (and thus bandwidth) for arbitrary-shaped antennas. As a by-product of this method, we extract the optimal current distribution as a function of antenna shape for design guidelines. We further extend this theory to find the Q limits of arbitrary-shaped antennas and antenna-platform systems, subject to specific radiation pattern requirements. In the second part of the thesis, we use the Theory of Characteristic Modes to optimize the location and excitation of single and multiple in-situ ESAs mounted on finite, sub-wavelength platforms as relates to unmanned aerial vehicles (UAVs). By properly analyzing the CMs of the supporting platform, we show that a complex, multivariate optimization problems can by radically simplified using CMs. Based on this capability, we present a new, systematic design methodology for location optimization of small antennas on-board finite platforms. The approach is shown to drastically reduce the time, computational cost, and complexity of a multi-element in-situ antenna design, as well as providing significant performance improvements in comparison to a typical single-antenna implementations.

Committee:

John Volakis, Dr. (Advisor); Kubilay Sertel, Dr. (Advisor); Robert Burkholder, Dr. (Committee Member)

Subjects:

Electrical Engineering

Keywords:

electrically small antennas; ESA; Q; quality factor; characteristic modes; method of moments; numerical methods

Guarendi, Andrew NNumerical Investigations of Magnetohydrodynamic Hypersonic Flows
Master of Science, University of Akron, 2013, Mechanical Engineering
Numerical simulations of magnetohydrodynamic (MHD) hypersonic flow are presented for both laminar and turbulent flow over a cylinder and flow entering a scramjet inlet. ANSYS CFX is used to carry out calculations for steady flow at hypersonic speeds (Mach number > 5). The low magnetic Reynolds number (<<1) calculated based on the velocity and length scales in this problem justifies the quasistatic approximation, which assumes negligible effect of velocity on magnetic fields. Therefore the governing equations employed in the simulations are the compressible Navier-Stokes and the energy equations with MHD-related source terms such as Lorentz force and Joule dissipation. Turbulence effects are accounted for when applicable and multiple turbulence models are compared. The results demonstrate the ability of the magnetic field to affect the flowfield, and variables such as location and magnitude of the applied magnetic field are examined. An examination of future work is provided through the implementation of a semi-discrete central scheme in-house code toward the solution of the Orszag-Tang vortex system.

Committee:

Abhilash Chandy, Dr. (Advisor); Scott Sawyer, Dr. (Committee Member); Alex Povitsky, Dr. (Committee Member)

Subjects:

Aerospace Engineering; Engineering; Fluid Dynamics; Mechanical Engineering

Keywords:

Hypersonic; Hypersonic Flow; Flow over a cylinder; Magnetohydrodynamic; MHD; Lorentz; Hypersonic MHD; Numerical Methods; CFD; Computational fluid dynamics; fluid dynamics; Aerospace;

Wang, SiliAn ABAQUS Implementation of the Cell-based Smoothed Finite Element Method Using Quadrilateral Elements
MS, University of Cincinnati, 2014, Engineering and Applied Science: Mechanical Engineering
This thesis report a work on an implementation of a Cell-based Smoothed Finite Element method (CS-FEM) using quadrilateral element (Q4) in the framework of the commercial software package ABAQUS®. The CS-FEM is one of the Smoothed Finite Element Method (S-FEM) models introduced by Dr. G.R. Liu and his colleagues in recent years. Because smoothing domains used by CS-FEM are within the element, it is known as the model closest to the standard FEM. User-defined Element subroutine (UEL) feature was proposed to be used to implant the CS-FEM model into ABAQUS. In this paper, a couple of UELs are constructed respectively for 2-dimentional (2D) problems using Q4 elements. To implant CS-FEM into ABAQUS, a custom input file and corresponding user subroutine are developed. Then the implementation is verified using a number of linear elastic problems that has analytical solutions. In this article, details on data input file and the user element subroutine construction are provided, which contribute the key ingredients of this implementation. Several numerical examples utilizing the subroutines are presented to demonstrate the features and accuracy of the developed ABAQUS CS-FEM Q4 user element, by comparison with the analytical and the ABAQUS solutions.

Committee:

Guirong Liu, Ph.D. (Committee Chair); Yijun Liu, Ph.D. (Committee Member); David Thompson, Ph.D. (Committee Member)

Subjects:

Mechanical Engineering

Keywords:

Cell-based Smoothed Finite Element Method;ABAQUS Standard;User defined Element;Numerical methods;CS FEM;UEL

Mitchell, Colin RaymondNumerical Simulation of Calcium Carbonate Formation
Master of Science, University of Akron, 2010, Applied Mathematics
Rimstone dams, formed by the deposition of calcium carbonate, arise in geologic systems, such as cave floors. These structures are formed by hydrodynamic and chemical interactions as mineral-rich water flows over a stable substrate. The depth of the water film, the reactions of several molecular species present in the water, and the profile of the substrate influence the potential for growth of mineral dams. A proposed model for the evolution of rimstone dams involves conditions for the free boundaries, the mineral substrate surface and the water surface, as well as the chemical system defining the reactions between the necessary chemicals to grow these structures. As the calcium carbonate deposits over time, both free boundaries are expected to evolve. Due to the complexity of the differential equations that arise in the modelling of this phenomenon, an analytic solution is difficult to obtain. Here, numerical methods will be employed to approximate a quantitative result, although on a system simplified by asymptotic assumptions. The equations that result can be solved numerically with simple finite-difference methods. The numerical growth of these structures qualitatively agree with the hypotheses surrounding the model and the natural occurences of rimstone dams.

Committee:

Curtis Clemons, Dr. (Advisor); Gerald Young, Dr. (Advisor); Kevin Kreider, Dr. (Committee Member)

Subjects:

Mathematics

Keywords:

rimstone travertine calcium carbonate formation dam numerical methods

Srinivasan, RaghuramMonte Carlo Alternate Approaches to Statistical Performance Estimation in VLSI Circuits
PhD, University of Cincinnati, 2014, Engineering and Applied Science: Computer Science and Engineering
Circuit simulation is an integral parts of the VLSI design process. Complex models have been developed to mimic the various phenomena that occur at the physical level; sophisticated numerical methods have also been simultaneously designed to handle the complexity of the mathematical models. As a result, large realistic models can be simulated accurately and efficiently. The SPICE simulation tool, with an extensive model library and extremely optimized numerical methods, is the current industry standard for circuit simulation. Recently though, due to the rapid reduction in feature sizes, values assumed for some of the parameters within the model during the design phase cannot be reproduced exactly during the fabrication phase. These aleatoric uncertainties in the model parameters induce non-determinism in the rest of the system variables. This has transformed the traditional circuit simulation problem into one of Statistical Performance Estimation (SPE). Statistical distributions are used to represent parameters and Monte Carlo (MC) type methods are used for analysis. While this approach is robust and easy to implement, it suffers from long analysis times due to its repetitive nature and, more importantly, the curse of dimensionality. The focus of this dissertation is to develop MC alternate methods for SPE: at the top level, we have developed two different methodologies using (a) interval arithmetic and (b) polynomial chaos expansions, with which we have developed intrusive methods to generate a system of equations that amenable to efficient SPE. The first approach uses interval valued variables to represent the uncertainties. Interval arithmetic follows special computation rules which allows for guaranteed enclosures to be produced. Since the computations are inherently pessimistic and prone to interval blowup, some transformations are necessary to contain these effects. We present a graph theoretic method to transform the DAE modeling the circuit into an ODE. We then use Taylor series expansion to produce a time marching method, this results in reliable guaranteed enclosures without repetitive runs of the deterministic simulation engine. Interval arithmetic, however, is incapable of producing statistical distributions which a MC type analysis can provide. In our second approach, we use polynomial chaos expansions to represent the the inherent and induced uncertainties in the system of equations. Galerkin conditions are used to project system to a finite dimensional basis gives us an extended deterministic DAE, the solution of which allows reintroduction of nondeterminism at a much cheaper cost. While such methods have been been developed for ODEs and PDEs, we have extended the theory to be able to analyze DAEs. In particular, we have shown that an extended form of MNA exists which allows for automatic equation extraction, and that the DAE index does not increase in the extended system. Finally, we have shown that nonlinear terms can also be accommodated in the method through sub-expansions. Experimental results show that the methods is accurate and efficient as compared to the MC method, and is also more immune to the curse of dimensionality.

Committee:

Fred Beyette, Ph.D. (Committee Chair); Harold Carter, Ph.D. (Committee Member); Wen Ben Jone, Ph.D. (Committee Member); Joy Moore, Ph.D. (Committee Member); Carla Purdy, Ph.D. (Committee Member); Ranganadha Vemuri, Ph.D. (Committee Member)

Subjects:

Engineering

Keywords:

VLSI;Circuit Simulation;Numerical Methods;Monte Carlo

Kerze, David JamesPerformance Characteristics of an Innovative Wind Power System
Master of Science in Mechanical Engineering, Cleveland State University, 2007, Fenn College of Engineering
This project entails a study of a wind energy recovery system that utilizes a unique three-dimensional spiral structure to amplify wind speed and direct it toward pluralities of turbines. The system is comprised of an outer spiral shell, internal support structure, turbines, and mechanisms for positioning the turbines to face the prevailing wind. Computational Fluid Dynamics (CFD) analyses were conducted to determine the wind speed amplification factors as a result of a simulated wind flow around the spiral structure. To ensure accuracy of the results, state of the art CFD techniques were applied using Gambit 2.2.30 and Fluent 6.2.16. Specifically, wind speed amplification factors were determined for 25ft and 30ft radius spiral shells. The velocity profiles of the wind flow around both spiral structures were obtained under a postulated 10mph wind speed. This resulted in a turbulent flow with a Reynolds number of 5,596,819. All analyses were run using “standard k-ε” turbulence model with the “near wall treatment” option “standard wall function”. A “y+” value of 50 was held constant in all vi simulations. The affect of the grid size on the accuracy of the results was examined. Convergence criterion was satisfied in each case. The 25ft radius spiral structure yielded an average velocity amplification factor of 1.524; while the 30ft radius resulted in an average amplification factor of 1.539. This particular information can help the designer of the system to select an appropriate overall shell size based not only on the mechanical efficiency, but also considering the cost and economical factors.

Committee:

Majid Rashidi (Advisor)

Keywords:

Wind; Turbines; Energy; Clean Energy; Green Energy; Wind Amplification; Fluent; Gambit; Wind Recovery; Reynolds Number; Mach Number; Velocity Magnitude; Velocity Contours; Spiral Structure; Numerical Methods

Brubaker, Lauren P.Completely Residual Based Code Verification
Master of Science, University of Akron, 2006, Applied Mathematics
Mathematical models of physical processes often include partial differential equations (PDEs). Oftentimes solving PDEs analytically is not feasible and a numerical method is implemented to obtain an approximate solution. Too often the assumption is made that the solution should be trusted when codes are prone to implementation errors. Code verification is a field of mathematics that shows the algorithm has been implemented without mistakes and has correctly solved the problem. Currently no one method of code verification is universally accepted. The Method of Manufactured Exact Solutions (MMES) is the most commonly used, but it has a considerable disadvantage of altering the code after verification. We have developed a new method, Completely Residual Based Code Verification (CRBCV), which does not require any modification. By using several solution methods, we have shown that CRBCV is dependable when verifying the heat equation with linear and nonlinear source terms and a frontal polymerization model.

Committee:

Laura Gross (Advisor)

Subjects:

Mathematics

Keywords:

Code verification; Partial Differential Equations; Numerical Methods; Method of Manufactured Exact Solutions; Frontal Polymerization; Heat Equation; Residual

Zhao, KezhongA domain decomposition method for solving electrically large electromagnetic problems
Doctor of Philosophy, The Ohio State University, 2007, Electrical Engineering
This dissertation presents a domain decomposition method as an effective and efficient preconditioner for frequency domain FEM solution of geometrically complex and electrically large electromagnetic problems. The method reduces memory requirements by decomposing the original problem domain into several non-overlapping and possibly repeatable sub-domains. At the heart of this research are the Robin-to-Robin map, the “cement” finite element coupling of non-conforming grids and the concept of duality paring. The Robin’s transmission condition is employed on interfaces between adjacent sub-domains to enforce continuity of electromagnetic fields and to ensure the sub-domain problems are well-posed. Through the introduction of cement variables, the meshes at the interface could be non-conformal which significantly relaxes the meshing procedures. By following the spirit of duality paring a symmetric system is obtained to better reflect physical nature of the problem. These concepts in conjunction with the so-called finite element tearing and interconnecting algorithm form the basic modules of the present domain decomposition method. To enhance the convergence of DDM solver, the Krylov solvers instead of classical stationary solvers are employed and studied. In order to account the radiation condition exactly thus eliminating spurious reflection, a boundary element formulation is hybridized with the present DD method, also through the aforementioned novel concepts. One of the special cases of present hybridization is the well known hybrid finite element and boundary element method. It will be shown that the proposed hybrid offers simultaneously: (1) symmetry, (2) modularity, (3) non-conformity between FEM and BEM domains, (4) free of internal resonance, and (5) natural and effective preconditioning scheme that guarantees spectral radius less or equal to one. Lastly this dissertation presents a DDM solution scheme for analyzing electromagnetic problems involving multiple separable scatterers. The method first decomposes the original problem into several disjoint sub-regions. In each sub-region, the domain decomposition method is further applied rendering geometrically complicated and electrically large sub-region problems tractable. The sub-regions communicate through the near-field Green’s function. To overcome the vast computational costs required in exchanging information between electrically large sub-regions, the adaptive cross approximation algorithm is adopted to expedite the process.

Committee:

Jin-Fa Lee (Advisor)

Keywords:

numerical methods; computational electromagnetics; domain decomposition method; finite element method; hybrid finite element and boundary element method; multi-region method

Iancu, Aniela KarinaNumerical methods for pricing basket options
Doctor of Philosophy, The Ohio State University, 2004, Mathematics
Most of the time, when pricing financial instruments, it is impossible to find closed form solutions for their values. Finding numerical solutions for the governing pricing equations becomes therefore an appealing approach to pricing, especially since powerful desktop computers are now available. In this paper we demonstrate how two of the main numerical methods known today—the finite differences method and the Monte Carlo simulation — can be used for pricing discretely measured lookback basket options. We also take a look at one of the most competitive markets today, The Individual Variable Annuity marketplace, at some of the currently sold death benefits and how they are related to the lookback put options.

Committee:

Bostwick Wyman (Advisor)

Subjects:

Mathematics

Keywords:

Numerical Methods; Option Pricing

Papp, John LaszloSIMULATION OF TURBULENT SUPERSONIC SEPARATED BASE FLOWS USING ENHANCED TURBULENCE MODELING TECHNIQUES WITH APPLICATION TO AN X-33 AEROSPIKE ROCKET NOZZLE SYSTEM
PhD, University of Cincinnati, 2000, Engineering : Aerospace Engineering
The successful application of CFD and turbulence modeling methods to an aerospike nozzle system first involves the successful simulation of its key flow components. This report addresses the task using the Chien low-Re k-? and the Yakhot et al. high-Re RNG k-? turbulence models. An improved implicit axis of symmetry boundary condition is also developed to increase stability and lower artificial dissipation. Grid adaptation through the SAGE post-processing package is used throughout the study. The RNG model, after low-Re modifications, and the Chien low-Re k-? model are applied to the supersonic axisymmetric base flow problem. Both models predict a peak recirculation velocity almost twice as large as experiment. The RNG model predicts a flatter base pressure and lower recirculation velocity more consistent with experimental data using less grid points than a comparable Chien model solution. The turbulent quantities predicted by both models are typical of other numerical results and generally under predict peak values obtained in experiment suggesting that too little turbulent eddy viscosity is produced. After several test cases, the full 3-D aerospike nozzle is simulated using both the Chien and modified RNG low-Re models. The Chien model outperforms the RNG model in all circumstances. The surface pressure predicted by the Chien model along the nozzle center-plane is very near experiment while mid-plane results are not as close but useful for design purposes. The lack of a thick boundary layer along the nozzle surface in RNG simulations is the cause of poor surface pressure comparisons. Although initial base flow comparisons between the model predictions and experiment are poor, the profiles are relatively flat. To accelerate the progress to a steady-state solution, a process involving the artificial lowering of the base pressure and subsequent iteration to a new steady state is undertaken. After several of these steps, the resulting steady-state base pressure is very near experimental values. The effect of a slight geometry change on the flow characteristics is also examined through different thruster nozzle faceplate designs. The result of the slight modification is a tremendous reduction in surface pressure and temperature caused by recirculation at the thruster nozzle exit without adverse nozzle performance losses.

Committee:

Karman Ghia (Advisor)

Subjects:

Engineering, Aerospace

Keywords:

Turbulence Modeling; Renormalization Group Theory (RNG); Supersonic separated base flows; Numerical Methods; Numerical Simulation