Recent events from the Magneto-Fluid Dynamics Seminar are listed below. To see the complete list of events, visit the seminar's main page, here.
Tuesday, March 31, 202011AM, Warren Weaver Hall 905
Ideal Plasma Response to Applied External Boundary Deformations in a Heliotron
Tony Cooper, Swiss Alps Fusion Energy
Tuesday, March 3, 202011AM, Warren Weaver Hall 905
Preserving Gauge Theoretic Structure in Plasma Simulations
Alexander Glasser, Princeton University
This work develops the geometric theory of charge conservation in particle-in-cell (PIC) plasma simulations. We define a new class of Hamiltonian algorithms---gauge-compatible splitting methods---that exactly preserve a Hamiltonian system's momentum map---even after time-discretization. We apply this general technique to design a novel, explicit, structure-preserving PIC splitting method, whose momentum map yields an exact local charge conservation law. We further study the preservation of Poincaré symmetry as a gauge symmetry of discrete dynamical fields, with an eye toward constructing plasma simulations that exactly conserve all ten relativistic energy-momenta.
Tuesday, February 25, 202011AM, Warren Weaver Hall 905
Implicit energy- and charge-conserving particle in cell methods on sparse grids
Lee Ricketson, Lawrence Livermore National Laboratory
The particle-in-cell (PIC) method has been widely used for half a century in the simulation of kinetic plasmas. The last decade has seen two new versions of the method that move toward overcoming long-standing challenges. First, the fully implicit, energy-conserving PIC scheme mitigates the so-called finite grid instability, allowing larger time-steps and, in many cases, coarser spatial resolution while retaining stability. Second, a sparse grid version of PIC was recently introduced that shows the potential to mitigate the curse of dimensionality, thereby dramatically reducing the number of simulated particles needed to achieve satisfactory statistical resolution. In this talk, we present a scheme that marries these two advances. We prove that the energy- and charge-conservation properties of implicit PIC can be carried over to sparse grids. Key here is the appropriate definition of the electrostatic potential. In so doing, we also generalize previous conservation results for implicit PIC to more general classes of field solvers and discuss potential applications of this generalization. Theoretical results are confirmed via numerical examples using a 2D electrostatic PIC code.
This is joint work with Guangye Chen (LANL).
*Work performed under the auspices of the U.S. Department of Energy by LLNL and LANL under contracts DE-AC52-07NA27344 and DE-AC52-06NA25396 and supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.
Tuesday, February 18, 202011AM, Warren Weaver Hall 905
High-Order Hybridized Discontinuous Galerkin methods and scalable solvers for Incompressible Resistive Magnetohydrodynamics
Sriramkrishnan Muralikrishnan, Paul Scherrer Institut, Switzerland
Synopsis:High-order methods are useful for simulating hyperbolic conservation laws commonly arising in many applications of fluid dynamics, electromagnetics and magnetohydrodynamics. They not only provide greater accuracy per computational cost when compared to lower order methods, but also a necessity to obtain correct dispersion properties. We consider here a particular high-order finite element method namely, hybridized discontinuous Galerkin method (HDG) suitable for current and future computing architectures. One of the attractive features of HDG methods is that they have lot fewer coupled unknowns at high orders in the context of steady state problems or time dependent problems with implicit time stepping. However, for practically large scale simulations the linear system arising from HDG methods still present a bottle neck till date.In this talk we present a block preconditioning strategy for incompressible visco-resistive magnetohydrodynamics (MHD) equations discretized with high-order HDG methods. MHD equations play an important role in modeling low Lundquist number liquid metal flows, high Lundquist number large-guide-field fusion plasmas and low flow-Mach-number compressible flows. They present several challenges in terms of nonlinearity, coupled fluid and magnetic physics, incompressibility constraints in both velocity and magnetic fields to name a few. For several 2D and 3D transient examples from MHD, including, but not limited to the island coalescence problem at high Lundquist numbers the preconditioner is robust. We also show strong and weak scalability of the block preconditioner up to 8192 cores in the Stampede2 supercomputer.
Tuesday, February 11, 202011AM, Warren Weaver Hall 905
Collective regimes of stimulated Brillouin scatter and collapse turbulence in laser fusion
Pavel Lushnikov, University of New Mexico
Laser fusion is intended to initiate the nuclear fusion reactions through compressing the thermonuclear target by powerful laser beams. These beams propagate through the surrounding plasma resulting in strongly nonlinear interactions. Perhaps the most important among these interactions is the stimulated Brillouin scattering (SBS) which couples the laser beam to the plasma density fluctuations and results in the numerous catastrophic collapse events during the laser beam propagation. The strong turbulence dominated by such nearly singular collapse event is considered. To suppress the number of such collapses, the expensive optical beams smoothing is used in the experimental laser fusion facilities which randomizes the phases of the laser beams. A statistical theory of SBS of such randomized laser beam propagation is developed. A collective regime of BSBS is found which has a much larger threshold than the classical threshold of a coherent beam in long-scale-length laser fusion plasma. The instability threshold is inside the typical parameter region of National Ignition Facility.