Sandia National Laboratories

From Flames to Fusion

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Plasma Application

Time-exposure photo of Sandia’s Z machine firing. Click image for larger version and more information

The group’s nonlinear solvers and preconditioner algorithms have been disseminated to the computational science community as part of the Trilinos solver framework, a parallel computing software package assembled at Sandia.  Now Shadid and his fellow researchers are extending their methods to plasmas — the stuff of stars and fusion energy.  The work could apply to astrophysics and plasma processing of advanced semiconductor and microelectromechanical systems (MEMS).  It also could help simulate plasma behavior in devices like ITER, the international fusion reactor project to be built in southern France; the National Ignition Facility (NIF) at DOE’s Lawrence Livermore National Laboratory; or Sandia’s own Z machine (see sidebar).

Sandia researchers Pavel Bochev and Jeff Banks work on the project with Shadid, Pawlowski and Tuminaro. They’re collaborating with Luis Chacón of Los Alamos National Laboratory, Dana Knoll of Idaho National Laboratory, and DOE Computational Science Graduate Fellow John Evans of the University of Texas.  The project marries methods the Sandia group devised with ones Chacón and Knoll have developed for magnetohydrodynamics (MHD) and extended magnetohydrodynamics (XMHD).

MHD studies how electrically conducting fluids move and are affected by magnetic fields.  The physics has similarities with those governing chemical transport and reaction — but with some twists.  “You add in electric and magnetic fields with Maxwell’s equations,” Shadid says.  “It makes the solution processes significantly more difficult.”

XMHD is trickier still.  Standard MHD simulations track just one type of fluid behavior, and couple ions and electrons so they behave as a single fluid.  XMHD brings in more complex electron dynamics, Chacón says. “Standard MHD is an approximation of what reality does, and the approximation involves several assumptions,” he adds. XMHD makes fewer assumptions, but “The price you pay is that it becomes a much more complicated system” to solve.

Like the Sandia group, Chacón, Knoll and their fellow researchers have focused on multigrid preconditioning methods with applications to MHD simulations.  In essence, their physics-based preconditioners determine which coupled physics equations govern the simulation’s time scale.

“We know that the coupling produces the problems in time scales and so we address those,” Chacón adds.  “That’s where the physics-based (approach) comes from.  You need to have the insights of what couplings are producing the time scales” and address those directly.  The preconditioning technique breaks the complex equation systems into smaller subsystems for multigrid solutions.

The Sandia group has used a similar physics-based preconditioner technique and applied it to low Mach-number fluid flows.  In effect, they decouple the equations into subsystems that can be more easily solved by multigrid methods. “We don’t decouple the actual iterative solver,” Shadid says.  “We decouple some of the physics in the preconditioners, which is just an approximation that gives us very fast, very good approximate solution.”

The method Chacón’s group uses also doesn’t assume any particular grid or mesh structure to discretize the governing equations.  The Sandia researchers use unstructured data grids, allowing them to discretize problems with complex geometries. The Los Alamos approach “readily generalizes to unstructured meshes,” Chacón adds.  “In principle there is a good marriage between the two. There is a direct translation to unstructured meshes.”

Shadid agrees: “It’s really an excellent collaboration.”

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