First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow

This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques.Comment: 22 pages, 8 figures submitted to Journal of Computational Physic

hp-FEM for Two-component Flows with Applications in Optofluidics

This thesis is concerned with the application of hp-adaptive finite element methods to a mathematical model of immiscible two-component flows. With the aim of simulating the flow processes in microfluidic optical devices based on liquid-liquid interfaces, we couple the time-dependent incompressible Navier-Stokes equations with a level set method to describe the flow of the fluids and the evolution of the interface between them

Mobile Technology Use by Rural Farmers and Herders

Mobile technology business leaders from many mobile technology companies practice digital apartheid when improving rural farmers\u27 communication and technology infrastructure in developing countries. Mobile technology business leaders who do not effectively plan mobile technology infrastructure deployment to rural farmers and herders are at a high risk of failure. Grounded in adaptive structuration theory of technology, the purpose of this qualitative multiple case study was to explore strategies mobile technology business leaders used to improve the mobile technology infrastructure for rural farmers and herders in the United Republic of Tanzania. The participants comprised three mobile technology business leaders from three different mobile technology businesses located in the United Republic of Tanzania who efficiently implemented business strategies to improve mobile technology infrastructure for rural farmers and herders of the United Republic of Tanzania. Data were collected from semistructured interviews, direct observations, and a review of company documents provided by participants. The thematic analysis process was used to analyze the data. Three themes emerged: cost of technology improvements, plans to implement infrastructure, and training and development. The key recommendations for mobile business leaders are building partnerships amongst mobile technology companies to raise capital and involve customers in their business models. The implication for positive social change includes improving access to mobile technology infrastructure to provide strategies for improving socioeconomic outcomes in and among poor rural farmers and herders\u27 communities

Hybrid First-Order System Least-Squares Finite Element Methods With The Application To Stokes And Navier-Stokes Equations

This thesis combines the FOSLS method with the FOSLL* method to create a Hybrid method. The FOSLS approach minimizes the error, e h = uh − u, over a finite element subspace, [special characters omitted], in the operator norm, [special characters omitted] ||L(uh − u)||. The FOSLL* method looks for an approximation in the range of L*, setting uh = L*wh and choosing wh ∈ [special characters omitted], a standard finite element space. FOSLL* minimizes the L 2 norm of the error over L*([special characters omitted]), that is, [special characters omitted] ||L*wh − u||. FOSLS enjoys a locally sharp, globally reliable, and easily computable a posterior error estimate, while FOSLL* does not. The Hybrid method attempts to retain the best properties of both FOSLS and FOSLL*. This is accomplished by combining the FOSLS functional, the FOSLL* functional, and an intermediate term that draws them together. The Hybrid method produces an approximation, uh, that is nearly the optimal over [special characters omitted] in the graph norm, ||eh[special characters omitted] := ½||eh|| 2 + ||Leh|| 2. The FOSLS and intermediate terms in the Hybrid functional provide a very effective a posteriori error measure. In this dissertation we show that the Hybrid functional is coercive and continuous in graph-like norm with modest coercivity and continuity constants, c0 = 1/3 and c1 = 3; that both ||eh|| and ||L eh|| converge with rates based on standard interpolation bounds; and that, if LL* has full H2-regularity, the L2 error, ||eh||, converges with a full power of the discretization parameter, h, faster than the functional norm. Letting ũh denote the optimum over [special characters omitted] in the graph norm, we also show that if superposition is used, then ||uh − ũ h[special characters omitted] converges two powers of h faster than the functional norm. Numerical tests on are provided to confirm the efficiency of the Hybrid method and effectiveness of the a posteriori error measure