A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

Leading from the Edge: Marginal Leadership at Cultural Crossroads

If a church reflects its larger community, it will have more dynamic interactions among different people. Current U.S. communities consist of very diverse people who have different socioeconomic and cultural backgrounds. Since the mid 20th century, various immigrant communities who have dissimilar cultural, religious, and linguistic traditions have accelerated the need of change in American churches. The drastic cultural change has demanded churches to equip their lay and clergy leaders with multicultural competencies for effective ministries.

My thesis explores imaginative leadership in cultural crossroads. Emphasizing the leadership imagination of cross-cultural ministry, I approach it in biblical, theological, and missional perspectives. In this dynamic cultural milieu, the study topic may help the church renew its ecclesial purpose by seeing cross-cultural ministry as a creative opportunity to reach out to more diverse people of God. I begin with a conceptual framework for cross-cultural ministry and cultural intelligence. Then I explain why cross-cultural ministry is significant and how it enhances the spirit of Christ Jesus. As I develop the thesis, I discuss leadership challenge and development in the cross-cultural ministry context. This thesis may contribute to equipping lay and clergy leaders by overcoming the homogeneous ‘in-group’ mindset in the church.

The primary focus is on developing marginal leadership of church in the post-Christendom era. Church leaders must creatively hold the tension between the current church context and Christian faith resources and seek a hopeful resolution as a third way through integrative thought process. While conventional leadership emphasizes a better choice out of the given options, marginal leadership takes time for integrative thought process to seek a new direction for the future. Conventional leaders take the center with their power, status, and prestige, but marginal leaders position themselves on the edge. Leading from the edge is a distinctive cross-cultural leadership and is based on the servant leadership of Jesus Christ who put himself as a servant for the marginalized. By serving and relating to others on the margin, this imaginative leadership may make appropriate changes desired in today’s American churches.

In addition to academic research, I looked into the realities of cross-cultural leadership in the local churches through congregational studies. I speculated that church leadership involves both laity and clergy and that it can be enhanced. All Christians are called to serve the Lord according to their gifts, and it is crucial for lay and clergy persons to develop their leadership character and skills. In particular, as humans are contextualized with their own cultures, church leaders often confront great challenges in cross-cultural or multicultural situations. Through critical thoughts and imaginative leadership strategies, however, they can overcome intrinsic human prejudice and obstacles.

Through the thesis project, I have reached four significant conclusions. First, cultural intelligence is an essential leadership capacity for all church leaders. As the church consists of more diverse cultural people today, its leaders need to have cultural competencies. In particular, cross-cultural leaders must be equipped with cultural intelligence. Cross-cultural ministry is not a simple byproduct of social change, but a creative strategy to open a door to bring God’s reconciliation among diverse people. Accordingly, church leaders are to be well prepared to effectively cope with the challenges of cultural interactions. Second, both lay and clergy leaders’ imaginative leadership is crucial for leading the congregation. While conventional leadership puts an emphasis on selecting a better choice based on the principle of opportunity cost, imaginative leaders critically consider the present church situations and Christian faith values together in integrative thoughts and pursue a third way as the congregation’s future hope. Third, cross-cultural leadership has a unique characteristic of leading from the edge and promotes God’s justice and peaceable relationships among different people. By leading the congregation from the edge, church leaders may experience the heart of Christ Jesus who became the friend of the marginalized. Fourth, the ‘homogeneous unit principle’ theory has its limit for today’s complex ‘inter-group’ community context. The church must be a welcoming and embracing faith community for all people. Cross-cultural ministry may become an entrance door for a more peaceable and reconciling life among different people. By building solidarity with others, the church may experience a kingdom reality.

This thesis focuses on the mission of the church and marginal leadership of church leaders in ever-changing cultural crossroads. The church becomes a hope in the broken and apathetic world, and Christians are called to build relationships inside and beyond the church. It is significant for church leaders to be faithfully present on the margin and relate to diverse people. By consistently positioning themselves on the margin, they can build relationships with new and diverse people and shape a faithful life pattern for others.