Alumni Project

The Applied Partial Differential Equations Center (APDEC): An Integrated Software Infrastructure Center for Block-Structured Adaptive Mesh Refinement

Principal Investigators: J. Bell, P. Colella, M. Berger, D. Brown, M. Minion, E.G. Puckett, C. Rutland. Collaborators: S. Jardin, R. Ryne, E. Esarey

The goal of this project is to develop a high-performance algorithmic and software framework for multi-scale problems in three important mission areas: magnetic fusion, accelerator design, and combustion, based on the use of block-structured adaptive mesh refinement (AMR) for representing multiple scales. We are taking an end-to-end approach to applying AMR to these problem areas, developing new self-contained simulation capabilities in collaboration with investigators in the applications fields.

Many important DOE applications can be described mathematically as solutions to partial differential equations exhibiting behavior on multiple length scales. Combustion for energy and transportation is dominated by the interaction of fluid dynamics and chemistry in localized flame fronts. Fueling of magnetic fusion devices involves the dispersion of material from small injected fuel pellets. The successful design of particle accelerators relies critically on the confinement of the charged beams to a small subset of the total volume.

In this project, we are developing a new class of simulation tools for these and other multi-scale problems. These tools are based on the use of block-structured adaptive mesh refinement (AMR) to represent multi-scale behavior. In this approach, the physical variables are discretized on a spatial grid consisting of nested rectangles of varying spatial resolution, organized into blocks (figure 1). This hierarchical discretization of space can adapt to changes in the solution to maintain a uniform level of accuracy throughout the simulation. We also can vary the temporal resolution to match the spatial resolution.

figure 1

Figure 1. An example of a block-structured refined grid in three dimensions. The individual grid cells are shown in white, and the black lines indicate the organization into blocks.

Finally, complex boundary geometries can be treated using an embedded boundary approach, in which the irregular boundary is represented by its intersection with the rectangular grid. The use of AMR can increase by orders of magnitude the range of length scales that can be resolved in a simulation, in comparison with traditional fixed-grid approaches.

The use of AMR requires the consideration of new mathematical, algorithmic, and software issues in order to represent the coupling between different scales. For that reason, we have taken an end-to-end approach, developing self-contained new simulation capabilities based on AMR. These include simulation codes for non-ideal magnetohydrodynamics problems arising in magnetic fusion (figure 2); AMR-PIC codes for computing particle-in-cell space charge effects for beam dynamics in accelerator design problems; an AMR embedded boundary code for simulating gas jets in laser-driven plasma-wakefield accelerators; and AMR combustion codes simulating for turbulent combustion in laboratory-scale flames.

figure 2

Figure 2. Calculation of magnetic reconnection using AMR. The boxes indicate the four nested levels of refinement to resolve the reconnection zone in the middle of the figure.

For the first three of these applications, we are in the process of validating the new capabilities, while in the case of combustion modeling, we have developed a complete AMR simulation capability and used it to perform simulations of a turbulent methane flame sheet with detailed chemical kinetics and transport.

Although these applications are quite diverse physically, there is considerable overlap in their mathematical structure. We have developed a component design for our software based on that common mathematical structure to maximize reuse across applications, as well as portability across platforms. We are also leveraging other related software being developed in this project by building interfaces that allows us to use these packages in our applications. Examples include the hypre linear solver package developed in the TOPS ISIC, and geometry definition and grid generation capabilities based on the
Cart3D grid generation package developed by NASA and geometry generation components developed in collaboration with the TSTT ISIC. Conversely, we are also developing interoperability standards for AMR codes, both to allow our applications collaborators to more easily integrate AMR capabilities into existing production codes, as well as to make our capabilities more accessible to other AMR developers (all of the code being produced under this project is fully-documented, and open-source).

figure 3 figure 3

Figure 3. An AMR embedded boundary grid for a gas-jet injector.

The principal focus of the project over the next year will be the application of the algorithms and software being developed here to specific multi-scale problems in the three applications areas. In magnetic fusion, we will use the AMR code we have recently developed to investigate the injection of fuel pellets. In accelerator modeling, we will integrate the AMR-PIC capability and other tools into the production accelerator simulation codes being developed by the SciDAC program. We will also complete the development of the tool for simulating transient gas jets to use in the design laser-driven plasma-wakefield accelerators. In combustion, we plan to extend our capabilities from modeling idealized flames sheets to the simulation of realistic laboratory-scale turbulent flames.

For further information on this subject contact:
Dr. Phillip Colella
Lawrence Berkeley National Laboratory
Phone: 510-486-5412
PColella@lbl.gov

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Updated: Monday, 21-Aug-2006 13:21:48 EDT