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We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the smallcell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L 1 for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.

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Over the last decade block-structured adaptive mesh refinement (SAMR) has found increasing use in large, publicly available codes and frameworks. SAMR frameworks have evolved along different paths. Some have stayed focused on specific domain areas, others have pursued a more general functionality, provid- ing the building blocks for a larger variety of applications. In this survey paper we examine a representative set of SAMR packages and SAMR-based codes that have been in existence for half a decade or more, have a reasonably sized and active user base outside of their home institutions, and are publicly available.The set consists of a mix of SAMR packages and application codes that cover a broad range of scientific domains. We look at their high-level frameworks, and their approach to dealing with the advent of radical changes in hardware architecture. The codes included in this survey are BoxLib, Cactus, Chombo, Enzo, FLASH, and Uintah.

We present a method for computing incompressible viscous flows in three dimensions using block-structured local refinement in both space and time. This method uses a projection formulation based on a cell-centered approximate projection, combined with the systematic use of multilevel elliptic solvers to compute increments in the solution generated at boundaries between refinement levels due to refinement in time. We use an L 0 -stable second-order semi-implicit scheme to evaluate the viscous terms. Results are presented to demonstrate the accuracy and effectiveness of this approach.

We present a method for solving Poisson and heat equations with discontinuous coefficients in two-and three-dimensions. It uses a Cartesian cutcell/embedded boundary method to represent the interface between materials, as described in Johansen & Colella (1998). Matching conditions across the interface are enforced using an approximation to fluxes at the boundary.Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 10 6 , thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed.An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.

Servant leadership in today's healthcare settings provides a unique avenue through which to assess leadership behaviors and the relationship to employee satisfaction and healthcare patient satisfaction measures. This study sought to determine the degree that leaders in community hospitals were perceived as servant leaders and the level of employee satisfaction at these rural community hospitals. Two hundred nineteen surveys were completed from 10 community hospitals. This research revealed that servant leadership and employee satisfaction are strongly correlated. In addition, servant leadership has a significant correlation between intrinsic satisfaction and HCAHPS scores. Further research can be extended to additional categories and geographic areas of the United States to determine how servant leadership, employee satisfaction, and HCAHPS are related. Hospital administrators should examine the findings of this study for possible implications to their leadership style and practice in determining how it may impact the organization they lead.