Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010. / Committee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Joseph. Part of the SMARTech Electronic Thesis and Dissertation Collection.

The Swedish defence agency (FOI) has developed a particle model (called Pello) that simulates the dispersion of aerosols and gases. At the boundaries, such as the ground, the particles can either reflect back into the domain (the atmosphere) or be absorbed. Which of the events that occurs is decided by a certain probability, which in the present model depends on mere physical properties. In this thesis we have investigated a newly proposed boundary behaviour which also depends on the time step used in the numerical simulations. We verified the accuracy of the new model by using a dispersion model with an explicit solution. To gain a better understanding of how important parameters at the boundary influence each other, we performed a sensitivity analysis. Simulations showed an overall improving concentration profile as the time step became smaller and the new model working well. The convergence order of the simulations was found to be close to 0.5. In this thesis we have shown that there exist an upper limit for the time step, which depends on the specific model. The present used time step at FOI does not have this versatile property. But having this upper limit for the time step close to the boundary, and a uniform time step can be time demanding. This lead us to the conclusion that an adaptive time step should be implemented.

Controlled cooling is an important part of steel production industry that affects the properties of the outcome steel. Many of the researches done in controlled cooling are experimental. Due to progress in the numerical techniques and high cost of experimental works in this field the numerical work seems more feasible. Heat transfer analysis is the necessary element of successful controlled cooling and ultimately achievement of novel properties in steel. Heat transfer on the surface of the plate normally contains different regimes such as film boiling, nucleate boiling, transition boiling and radiation heat transfer. This makes the analysis more complicated. In order to perform the heat transfer analysis often empirical correlations are being used. In these correlations the velocity and pressure within the fluid domain is involved. Therefore in order to obtain a better understanding of heat transfer process, study of hydrodynamics of the fluid becomes necessary. Circular jet due to its high efficiency has been used vastly in the industry. Although some experimental studies of round jet arrays have been done, yet the characteristics of a single jet with industrial geometric and flow parameters on the surface of a flat plate is not fully understood. Study of hydrodynamics of the jet impingement is the first step to achieve better understanding of heat transfer process. Finite element method as a popular numerical method has been used vastly to simulate different domains. Traditional approaches of finite element method, Lagrangian and Eulerian, each has its own benefits and drawbacks. Lagrangian approach has been used widely in solid domains and Eulerian approach has been widely used in fluid fields. Jet impingement problem, due to its unknown free surface and the change in the boundary, falls in the category of special problems and none of the traditional approaches is suitable for this application. The Arbitrary Lagrangian Eulerian (ALE) formulation has emerged as a technique that can alleviate many of the shortcomings of the traditional Lagrangian and Eulerian formulations in handling these types of problems. Using the ALE formulation the computational grid need not adhere to the material (Lagrangian) nor be fixed in space (Eulerian) but can be moved arbitrarily. Two distinct techniques are being used to implement the ALE formulation, namely the operator split approach and the fully coupled approach. This thesis presents a fully coupled ALE formulation for the simulation of flow field. ALE form of Navier-Stokes equations are derived from the basic principles of continuum mechanics and conservation laws in the fluid. These formulations are then converted in to ALE finite element equations for the fluid flow. The axi-symmetric form of these equations are then derived in order to be used for jet impingement application. In the ALE Formulation as the mesh or the computational grid can move independent of the material and space, an additional set of unknowns representing mesh movement appears in the equations. Prescribing a mesh motion scheme in order to define these unknowns is problem-dependent and has not been yet generalized for all applications. After investigating different methods, the Winslow method is chosen for jet impingement application. This method is based on adding a specific set of partial differential Equations(Laplace equations) to the existing equations in order to obtain enough equations for the unknowns. Then these set of PDEs are converted to finite element equations and derived in axi-symmetric form to be used in jet impingement application. These equations together with the field equations are then applied to jet impingement problem. Due to the number of equations and nonlinearity of the field equations the solution of the problem faces some challenges in terms of convergence characteristics and modeling strategies. Some suggestions are made to deal with these challenges and convergence problems. Finally the numerical treatment and results of analyzing hydrodynamics of the Jet Impingement is presented. The work in this thesis is confined to the numerical simulation of the jet impingement and the specifications of an industrial test setup only have been used in order to obtain the parameters of the numerical model.

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This thesis explores three consolidation problems derived from the daily operations of major international airfreight forwarders. First, we study the freight forwarder's unsplittable shipment planning problem in an airfreight forwarding network where a set of cargo shipments have to be transported to given destinations. We provide mixed integer programming formulations that use piecewise-linear cargo rates and account for volume and weight constraints, flight departure/arrival times, as well as shipment-ready times. After exploring the solution of such models using CPLEX, we devise two solution methodologies to handle large problem sizes. The first is based on Lagrangian relaxation, where the problems decompose into a set of knapsack problems and a set of network flow problems. The second is a local branching heuristic that combines branching ideas and local search. The two approaches show promising results in providing good quality heuristic solutions within reasonable computational times, for difficult and large shipment consolidation problems. Second, we further explore the freight forwarder's shipment planning problem with a different type of discount structure - the system-wide discount. The forwarder's cost associated with one flight depends not only on the quantity of freight assigned to that flight, but also on the total freight assigned to other flights operated by the same carrier. We propose a multi-commodity flow formulation that takes shipment volume and over-declaration into account, and solve it through a Lagrangian relaxation approach. We also model the "double-discount" scheme that incorporates both the common flight-leg discount (the one used in the unsplittable shipment problem) and the system-wide discount offered by cargo airlines. Finally, we focus on palletized loading using unit loading devices (ULDs) with pivots, which is different from what we assumed in the previous two research problems. In the international air cargo business, shipments are usually consolidated into containers; those are the ULDs. A ULD is charged depending on whether the total weight exceeds a certain threshold, called the pivot weight. Shipments are charged the under-pivot rate up to the pivot weight. Additional weight is charged at the over-pivot rate. This scheme is adopted for safety reasons to avoid the ULD overloading. We propose three solution methodologies for the air-cargo consolidation problem under the pivot-weight (ACPW), namely: an exact solution approach based on branch-and-price, a best fit decreasing loading heuristic, and an extended local branching. We found superior computational performance with a combination of the multi-level variables and a relaxation-induced neighborhood search for local branching.

Thesis (Ph.D.)--University of Rhode Island, 2006. / Includes bibliographical references (leaves 130-134).

Thesis (M.Sc.). / Written for the Dept. of Atmospheric and Oceanic Sciences. Title from title page of PDF (viewed 2008/05/13). Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 134-143).

Thesis (M.S.)--California Polytechnic State University, 2010. / Title from PDF title page; viewed on May 20, 2010. Major professor: Faysal Kolkailah, Ph.D. "Presented to the faculty of California Polytechnic State University, San Luis Obispo." "In partial fulfillment of the requirements for the degree [of] Master of Science in Aerospace Engineering." "April 2010." Includes bibliographical references (p. 136-140).