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. The algorithmic approach we are taking is based on the use of finite-difference methods on structured grids combined with 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. 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.

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 AMR fluid simulation codes for turbulent combustion in laboratory-scale flames and for non-ideal magnetohydrodynamics problems arising in magnetic fusion; AMR-PIC codes for computing particle-in-cell space charge effects for beam dynamics in accelerator design problems; and an AMR embedded boundary code for simulating gas jets in laser-driven plasma-wakefield accelerators. These efforts are supported by an extensive activity in the development of software frameworks for AMR and embedded boundary methods. There are also efforts to develop new algorithmic approaches for solving these problems, including new methods for treating complex geometries, and higher-order accurate methods.

Participants

Management Documents

• Proposal
• 2003 Status Report