Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 23 for “"Method of lines"”.
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Application of a Numerical Method and Optimal Control Theory to a Partial Differential Equation Model for a Bacterial Infection in a Chronic Wound
<p>In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange …
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Hydraulic properties of subglacial sediment determined from the mechanical response of water-filled boreholes
The hydraulic properties of basal sediments must be known if the surge mechanism of soft-bedded glaciers is to be understood. Freezing of water-filled boreholes drives water into the subglacial bed and the associated pressure effects give information about subglacial hydraulic properties. A …
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A numerical method for systems of ordinary differential equations
… the utility, generality and simplicity of a new computational method of solving systems of ordinary differential equations. The central idea of this new method revolves around our ability to generate a numerical approximation of the general solution of systems of linear differential …
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Mathematical modeling, simulation, and optimal design of pharmaceutical crystallizers
… as tablets with precisely tunable quantities of active pharmaceutical ingredients. The mathematical modeling and simulation of crystallization processes are useful in systems engineering, with the key conservation equation for the particle size distribution being a partial differential …
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A Discontinuous Galerkin Method for Higher-Order Differential Equations Applied to the Wave Equation
We propose a new discontinuous finite element method for higher-order initial value problems where the finite element solution exhibits an optimal convergence rate in the L2- norm. We further show that the q-degree discontinuous solution of a differential equation of order m and its first …
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Lightly-Implicit Methods for the Time Integration of Large Applications
… engineering applications require the solution of large systems of initial value problems arising from method of lines discretization of partial differential equations. For systems with widely varying time scales, or with complex physical dynamics, implicit time integration schemes are preferred …
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Adaptive stable finite-element methods for the compressible Navier-Stokes equations
… a useful predictive tool for a wide range of engineering applications. Of particular interest in this thesis are computational methods for solving the problem of compressible fluid flow around aerodynamic configurations. A finite element method is presented for solving the compressible …
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Numerical relativity in black hole spacetimes
This thesis is concerned with the development of better techniques for the 3 + 1 numerical relativity study of black hole spacetimes. The main result of this thesis is the development of a new technique for avoiding singularities in such spacetimes. In this technique the slices are allowed to …
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Numerical Methods for Parameter Estimation and Optimal Control of the Red River Network
In this thesis efficient numerical methods for the simulation, the parameter estimation, and the optimal control of the Red River system are presented. The model of the Red River system is based on the Saint-Venant equation system, which consists of two nonlinear first-order hyperbolic Partial …
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Large Eddy Simulation of Supersonic Twin-Jet Impingement Using a Fifth-Order WENO Scheme
… simulation (LES). The numerical model consists of two parallel axisymmetric jets of diameter 𝐷*, 3𝐷* apart, issuing from a plane which is at a distance H*=4𝐷* above the ground. The jet diameter 𝐷*, mean velocity 𝑊ₒ*, mean density 𝜌ₒ* and mean temperature 𝑇ₒ* at the jet center in the exit plane …
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A Numerical Method for Extended Boussinesq Shallow-Water Wave Equations
The accurate numerical simulation of wave disturbance within harbours requires consideration of both nonlinear and dispersive wave processes in order to capture such physical effects as wave refraction and diffraction, and nonlinear wave interactions such as the generation of harmonic waves. The …
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Multiscale Modeling of an Industrial Nylon-6 Leacher
This thesis presents a multiscale model of an industrial nylon-6 leacher. We develop several models at various spatial scales and implement them together in a simplistic, efficient way to develop an overall leacher model. We solve dynamic transport differential equations using the finite-volume …
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Time Integration Methods for Large-scale Scientific Simulations
The solution of initial value problems is a fundamental component of many scientific simulations of physical phenomena. In many cases these initial value problems arise from a method of lines approach to solving partial differential equations, resulting in very large systems of equations that …
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Nonconforming Immersed Finite Element Methods for Interface Problems
… are carried out over domains consisting of multiple materials separated by curves/surfaces. If partial differential equations (PDEs) are used to model these simulations, it usually leads to the so-called interface problems of PDEs whose coefficients are discontinuous. In this …
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Mathematical Modelling of Fibre Fabrication; Coupling Heat Transport with Fluid Flow in Extrusion
… a die to give a preform, the macroscopic version of the fibre, which is stretched either by pulling with a given force or by gravitational stretching. The extruded preform is then reheated as it is fed slowly into the furnace region of a draw tower, from which it is pulled at a fast speed to yield …
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Learning Nonlinear Dynamics: Methods and Applications
Accurate modeling of dynamical systems through differential equations is essential for scientific prediction and prescriptive control. Traditional model development, which relies on expert knowledge, parameter fitting and validation, is often iterative, time-consuming, and complicated by real-world …
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Stability analysis of a bilayer contained within a cylindrical tube
… lung are coated with a liquid bilayer consisting of a serous layer adjacent to a more viscous mucus layer which is contiguous with the air core. An instability due to surface tension at the interfaces may lead to the formation of a liquid plug that blocks the passage of air. This is known as …
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Numerical Methods for Simulation and Optimization of Chemically Reacting Flows in Catalytic Monoliths
The aim of this work is to develop numerical methods and software for simulation and optimization of complex processes in catalytic monoliths to achieve better understanding of the physic-chemical processes in catalytic reactors. The fluid dynamics are modelled by the boundary layer equations …
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Inventarisasi pohon pelindung dan potensinya sebagai penyerap karbon dioksida (CO2) serta penyimpan karbon di Jalan Raya Kota Malang
… can be characterized by the surface temperature of the earth. The increasing of global temperatures caused by increasing CO2 in the atmosphere, followed by increasing of the number of transportation, population, industry, and the feeling of trees. Increasing of CO2 gas are produced in urban …
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