We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout. © 2011. The American Astronomical Society. All rights reserved.

The Antarctic Ice Sheet (AIS) remains the largest uncertainty in projections of future sea level rise. A likely climate-driven vulnerability of the AIS is thinning of floating ice shelves resulting from surface-melt-driven hydrofracture or incursion of relatively warm water into subshelf ocean cavities. The resulting melting, weakening, and potential ice shelf collapse reduces shelf buttressing effects. Upstream ice flow accelerates, causing thinning, grounding-line retreat, and potential ice sheet collapse. While high-resolution projections have been performed for localized Antarctic regions, full-continent simulations have typically been limited to low-resolution models. Here we quantify the vulnerability of the entire present-day AIS to regional ice shelf collapse on millennial timescales treating relevant ice flow dynamics at the necessary ∼1-km resolution. Collapse of any of the ice shelves dynamically connected to the West Antarctic Ice Sheet (WAIS) is sufficient to trigger ice sheet collapse in marine-grounded portions of the WAIS. Vulnerability elsewhere appears limited to localized responses.

Water flowing under ice sheets and glaciers can have a strong influence on ice dynamics, particularly through pressure changes, suggesting that a comprehensive ice sheet model should include the effect of basal hydrology. Modeling subglacial hydrology remains a challenge, however, mainly due to the range of spatial and temporal scales involved - from subglacial channels to vast subglacial lakes. Additionally, networks of subglacial drainage channels dynamically evolve over time. To address some of these challenges, we have developed an adaptive mesh refinement (AMR) model based on the Chombo software framework. We extend the model proposed by with a small but significant change to accommodate the transition from unresolved to resolved flow features. We handle the strong nonlinearities present in the equations by resorting to an efficient nonlinear full approximation scheme multigrid (FAS-MG) algorithm. We outline the details of the algorithm and present convergence analysis results demonstrating its good performance. Additionally, we present results validating our approach, using test cases from the Subglacial Hydrology Model Intercomparison Project (SHMIP) . We finish by presenting a more complex, 100 km-by-100 km synthetic test case with peaks and valleys that we use to investigate the effective pressure distribution as the number of AMR levels increases. These preliminary results suggest that a minimum spatial resolution is needed to properly capture channel features, but additional work is required to precisely quantify this and its impact on accurately modeling the coupled ice sheet-hydrology system. The efficiency of our approach, relying on localized refinement, is also demonstrated. Future work will include coupling the SUbglacial Hydrology MOdel (SUHMO) with the BISICLES AMR ice sheet model , both built on the same numerical framework.

Structured-grid adaptive mesh refinement (SAMR) is an approach to mesh generation that supports structured access to data and adaptive mesh refinement for discretized partial differential equations (PDEs). Solution algorithms often require that an inverse of an operator be applied, a system of algebraic equations must be solved, and this process is often the primary computational cost in an application. SAMR is well suited to geometric multigrid solvers, which can be effective, but often do not adapt well to complex geometry including material coefficients. Algebraic multigrid (AMG) is more robust in the face of complex geometry, in both boundary conditions and internal material interfaces. AMG requires a stored matrix linearization of the operator. We discuss an approach, and an implementation in the Chombo block-structured AMR framework, for constructing composite grid matrices from a SAMR hierarchy of grids for use in linear solvers in the PETSc numerical library. We consider a case study with the Chombo-based BISICLES ice sheet modeling application.

Inaccurate representations of iceberg calving from ice shelves are a large source of uncertainty in mass-loss projections from the Antarctic ice sheet. Here, we address this limitation by implementing and testing a continuum damage-mechanics model in a continental scale ice-sheet model. The damage-mechanics formulation, based on a linear stability analysis and subsequent long-wavelength approximation of crevasses that evolve in a viscous medium, links damage evolution to climate forcing and the large-scale stresses within an ice shelf. We incorporate this model into the BISICLES ice-sheet model and test it by applying it to idealized (1) ice tongues, for which we present analytical solutions and (2) buttressed ice-shelf geometries. Our simulations show that the model reproduces the large disparity in lengths of ice shelves with geometries and melt rates broadly similar to those of four Antarctic ice shelves: Erebus Glacier Tongue (length ∼ 13 km), the unembayed portion of Drygalski Ice Tongue (∼ 65 km), the Amery Ice Shelf (∼ 350 km) and the Ross Ice Shelf (∼ 500 km). These results demonstrate that our simple continuum model holds promise for constraining realistic ice-shelf extents in large-scale ice-sheet models in a computationally tractable manner.

The solidification of a binary alloy results in the formation of a porous mushy layer, within which spontaneous localisation of fluid flow can lead to the emergence of features over a range of spatial scales. We describe a finite volume method for simulating binary alloy solidification in two dimensions with local mesh refinement in space and time. The coupled heat, solute, and mass transport is described using an enthalpy method with flow described by a Darcy-Brinkman equation for flow across porous and liquid regions. The resulting equations are solved on a hierarchy of block-structured adaptive grids. A projection method is used to compute the fluid velocity, whilst the viscous and nonlinear diffusive terms are calculated using a semi-implicit scheme. A series of synchronization steps ensure that the scheme is flux-conservative and correct for errors that arise at the boundaries between different levels of refinement. We also develop a corresponding method using Darcy's law for flow in a porous medium/narrow Hele-Shaw cell. We demonstrate the accuracy and efficiency of our method using established benchmarks for solidification without flow and convection in a fixed porous medium, along with convergence tests for the fully coupled code. Finally, we demonstrate the ability of our method to simulate transient mushy layer growth with narrow liquid channels which evolve over time.

The US Department of Energy Office of Science and the National Nuclear Security Administration initiated the Exascale Computing Project (ECP) in 2016 to prepare mission-relevant applications and scientific software for the delivery of the exascale computers starting in 2023. The ECP currently supports 24 efforts directed at specific applications and six supporting co-design projects. These 24 application projects contain 62 application codes that are implemented in three high-level languages—C, C++, and Fortran—and use 22 combinations of graphical processing unit programming models. The most common implementation language is C++, which is used in 53 different application codes. The most common programming models across ECP applications are CUDA and Kokkos, which are employed in 15 and 14 applications, respectively. This article provides a survey of the programming languages and models used in the ECP applications codebase that will be used to achieve performance on the future exascale hardware platforms.

Coupled ice sheet-ocean models capable of simulating moving grounding lines are just becoming available. Such models have a broad range of potential applications in studying the dynamics of marine ice sheets and tidewater glaciers, from process studies to future projections of ice mass loss and sea level rise. The Marine Ice Sheet-Ocean Model Intercomparison Project (MISOMIP) is a community effort aimed at designing and coordinating a series of model intercomparison projects (MIPs) for model evaluation in idealized setups, model verification based on observations, and future projections for key regions of the West Antarctic Ice Sheet (WAIS).

Here we describe computational experiments constituting three interrelated MIPs for marine ice sheet models and regional ocean circulation models incorporating ice shelf cavities. These consist of ice sheet experiments under the Marine Ice Sheet MIP third phase (MISMIP+), ocean experiments under the Ice Shelf-Ocean MIP second phase (ISOMIP+) and coupled ice sheet-ocean experiments under the MISOMIP first phase (MISOMIP1). All three MIPs use a shared domain with idealized bedrock topography and forcing, allowing the coupled simulations (MISOMIP1) to be compared directly to the individual component simulations (MISMIP+ and ISOMIP+). The experiments, which have qualitative similarities to Pine Island Glacier Ice Shelf and the adjacent region of the Amundsen Sea, are designed to explore the effects of changes in ocean conditions, specifically the temperature at depth, on basal melting and ice dynamics. In future work, differences between model results will form the basis for the evaluation of the participating models.

This report presents results from the DOE-sponsored workshop titled, Advancing X-Cutting Ideas for Computational Climate Science Workshop,'' known as AXICCS, held on September 12--13, 2016 in Rockville, MD. The workshop brought together experts in climate science, computational climate science, computer science, and mathematics to discuss interesting but unsolved science questions regarding climate modeling and simulation, promoted collaboration among the diverse scientists in attendance, and brainstormed about possible tools and capabilities that could be developed to help address them. Emerged from discussions at the workshop were several research opportunities that the group felt could advance climate science significantly. These include (1) process-resolving models to provide insight into important processes and features of interest and inform the development of advanced physical parameterizations, (2) a community effort to develop and provide integrated model credibility, (3) including, organizing, and managing increasingly connected model components that increase model fidelity yet complexity, and (4) treating Earth system models as one interconnected organism without numerical or data based boundaries that limit interactions. The group also identified several cross-cutting advances in mathematics, computer science, and computational science that would be needed to enable one or more of these big ideas. It is critical to address the need for organized, verified, and optimized software, which enables the models to grow and continue to provide solutions in which the community can have confidence. Effectively utilizing the newest computer hardware enables simulation efficiency and the ability to handle output from increasingly complex and detailed models. This will be accomplished through hierarchical multiscale algorithms in tandem with new strategies for data handling, analysis, and storage. These big ideas and cross-cutting technologies for enabling breakthrough climate simulation advancements also need the "glue" of outreach and learning across the scientific domains to be successful. The workshop identified several strategies to allow productive, continuous engagement across those who have a broad knowledge of the various angles of the problem. Specific ideas to foster education and tools to make material progress were discussed. Examples include follow-on cross-cutting meetings that enable unstructured discussions of the types this workshop fostered. A concerted effort to recruit undergraduate and graduate students from all relevant domains and provide them experience, training, and networking across their immediate expertise is needed. This will broaden and expand their exposure to the future needs and solutions, and provide a pipeline of scientists with a diversity of knowledge and know-how. Providing real-world experience with subject matter experts from multiple angles may also motivate the students to attack these problems and even come up with the missing solutions.