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Many problems in uid dynamics have domains with complicated internal or external boundaries of the ow. Here we present a method for calculating time-dependent incompressible inviscid ow using a \Cartesian grid" approach for representing geometry. In this approach, the body is represented as an interface embedded in a regular Cartesian mesh. The basic algorithm is a fractional-step projection method based on an approximate projection. The advection step is based on a Cartesian grid algorithm for compressible ow, in which the discretization of the body near the ow uses a volume-of-uid representa

Axisymmetric numerical simulations continue to provide insight into how the structure, dynamics, and maximum windspeeds of tornadoes, and other convectively-maintained vortices, are influenced by the surrounding environment. This work is continued with a new numerical model of axisymmetric incompresible flow that incorporates adaptive mesh refinement. The model dynamically increases or decreases the resolution in regions of interest as determined by a specified refinement criterion. Here, the criterion used is based on the cell Reynolds number , so that the flow is guaranteed to be laminar on the scale of the local grid spacing.The model is used to investigate how the altitude and shape of the convective forcing, the size of the domain, and the effective Reynolds number (based on the choice of the eddy viscosity ν) influence the structure and dynamics of the vortex. Over a wide variety of domain and forcing geometries, the vortex Reynolds number Γ/ν (the ratio of the far-field circulation to the eddy viscosity) is shown to be the most important parameter for determining vortex structure and behavior. Furthermore, it is found that the vertical scale of the convective forcing only affects the vortex inasmuch as this vertical scale contributes to the total strength of the convective forcing. The horizontal scale of the convective forcing, however, is found to be the fundamental length scale in the problem, in that it can determine both the circulation of the fluid that is drawn into the vortex core, and also influences the depth of the swirling boundary layer. Higher mean windspeeds are sustained as the eddy viscosity is decreased; however, it is observed that the highest windspeeds are found in the high-swirl, two-celled vortex regime rather than in the low-swirl, one-celled regime, which is contrast with some previous results.

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of ECP applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modelling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multi-physics algorithms. AMReX supports algorithms that solve systems of partial differential equations (PDEs) in simple or complex geometries, and those that use particles and/or particle-mesh operations to represent component physical processes. In this paper, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of acceleratorbased architectures for a variety of different applications.

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