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Mesh Generation and Adaptivity Tools from the Terascale Simulation Tools and Technology (TSTT) Center

PIs: J. Glimm^1,2, D. Brown³, L. Freitag⁴, Co-PIs: E. D’Azevedo⁵, P. Fischer⁶, P. Knupp⁴, X.L. Li², M. Shephard⁷, H. Trease⁸, Affiliated Researchers: J. Drake⁵ (Climate), K.Ko⁹ (Accelerators), S. Jardin¹⁰ (CEMM), C. Tzanos⁶ (Combustion)

¹Brookhaven National Laboratory, ²State University of New York at Stony Brook, ³Lawrence Livermore National Laboratory, ⁴Sandia National Laboratories, ⁵Oak Ridge National Laboratory, ⁶Argonne National Laboratory, ⁷Rensselear Polytechnic Institute, ⁸Pacific Northwest National Laboratory, ⁹Stanford Linear Accelerator, ¹⁰Princeton Plasma Physics Laboratory

Summary

Our goal is to improve the accuracy and fidelity of PDE-based simulations by bringing modern mesh generation and adaptive mesh tools to the application scientist. These tools, however, often have a level of software implementation difficulty that has limited their usage. To address this, we are working directly with SciDAC application teams to enhance mesh generation techniques for complex geometries, improve mesh quality analysis and control, and insert sophisticated adaptive technologies directly into their simulations.

Vision. Many science simulation problems, including those in the SciDAC program, call for enhanced mesh generation and adaptive mesh refinement technologies. Complex geometrical domains, the need for enhanced resolution in regions where the solution is rapidly changing, or requirements on the quality of the underlying mesh all complicate the numerical simulation of applications based on the solution of partial differential equations (PDEs). The TSTT center is working closely with several SciDAC projects and with related application areas and groups to ensure that existing mesh technologies are utilized to their fullest extent. Our primary efforts are focused on accelerator design, climate, combustion and biology.

Adaptive Mesh Technologies. Most simulation problems contain subregions of greater complexity, difficulty, and importance that require enhanced resolution. Adaptive mesh tools allow the focusing of simulation effort where it is most needed, and we are using these tools in climate and combustion applications.

Climate. Atmospheric flows over mountain ranges respond dynamically to the variations in height these ranges present. The flow dynamics is thus inherently more complex near such regions, and as a result the simulation of the flow is more difficult there. Adaptive meshing will concentrate the computational effort unequally by placing extra mesh points to increase simulation resolution as needed near the mountain ranges. As a result, the mesh itself reflects the global map of the world, with the mountain ranges highlighted through a dense set of mesh lines. See Fig. 1. Climate scientists are using these new meshes to obtain improved accuracy for their climate simulations.

Combustion. The combustion effort has emphasized the break up of a diesel jet into spray, again a problem with highly localized and important solution details for which adaptive methods will prove very helpful. See Fig. 2. We anticipate obtaining a validated, predictive model for the formation of spray, thereby creating a new capability for diesel engine design.

Enhanced Mesh Generation Capabilities. In many applications, the geometrical complexity of the computational domain leads to difficulties in the mesh generation process that the TSTT center is working to address. Of particular note are our efforts in the accelerator design and biology applications.

Accelerator design. Accelerating cavities and beamline components have complex boundaries which complicates the process of generating high-quality, computational meshes. Unfort-unately, the solution algorithm preferred for this problem performs inefficiently on highly irregular or distorted meshes. We have been working closely with accelerator scientists to help decrease the time needed to generate an initial mesh for these geometries and to understand the relationship between the mesh quality and the stability of the numerical solution scheme. We have characterized the aspects of mesh quality that most affect simulation run time and will work to provide a tool that improves the mesh quality with respect to these characteristics. An alternate route, which we are pursuing in parallel, is to improve the solution algorithm, to reduce its sensitivity to the mesh quality.

Biology. Our efforts in biology have focused on the generation of meshes for complex geometries defined by experimental data, such as an MRI image of a rat nose, throat and lung cavity. The resulting simulations are the first ever conducted in such a realistic geometry, and offer new insight into the biodynamics of the pulmonary system.

A new mode for simulation science. The SciDAC team approach has transformed the manner in which we conduct science. Collaborations, interactions, end use relevance, and integration with the (team) work of others have been given a proper and increased emphasis.

Future plans. Our plans call for continued close interaction with key application teams. Their continued need for mesh adaptivity is far from being realized. There are, in fact, a large number of tools and ideas available for mesh adaptivity, and more of these will be explored and tested in key application areas in the future. The mesh generation and mesh quality improvement tools will be enhanced to better solve the problems arising in our application partnerships. In other cases, the requirements of the applications will prompt the development of new adaptive meshing capabilities. For example we plan to use adaptive techniques in the fusion application to better resolve highly focused gradients in the magnetic field and plasma variables.

Fig. 1. Mesh concentration over the Himalayas (shown in red) and Andes (not visible in this view) allow improved climate simulations.

Fig. 2. Breakup of diesel fuel injection jet into spray prior to combustion Density color coded

Further information: http://www.tstt-scidac.org
James Glimm, Brookhaven National Laboratory,
Phone: 631-333-8155, glimm@bnl.gov
David L. Brown, Lawrence Livermore National Laboratory,
Phone: 925-424-3557, dbl@llnl.gov
Lori Freitag Diachin, Sandia National Laboratories,
Phone: 505-284-9711, ladiach@sandia.gov

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