A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

Abstract

A continuum kinetic model for plasma based on the Vlasov-Maxwell system for multiple particle species is developed. Consideration is added for boundary conditions in a truncated velocity domain and supporting wall interactions. A scheme to scale the velocity domain for multiple particle species with different temperatures and particle mass while sharing one computational mesh is described. A method for assessing the degree to which the kinetic solution differs from a Maxwell-Boltzmann distribution is introduced and tested on a thoroughly studied test case.The discontinuous Galerkin numerical method is extended for efficient solution of hyperbolic conservation laws in five or more particle phase-space dimensions using tensor-product hypercube elements with arbitrary polynomial order. A scheme for velocity moment integration is integrated as required for coupling between the plasma species and electromagnetic waves.A new high performance simulation code WARPM is developed to efficiently implement the model and numerical method on emerging many-core supercomputing architectures.WARPM uses the OpenCL programming model for computational kernels and task parallelism to overlap computation with communication. WARPM single-node performance and parallel scaling efficiency are analyzed with bottlenecks identified guiding future directions for the implementation.The plasma modeling capability is validated against physical problems with analytic solutions and well established benchmark problems.

Physics-Based-Adaptive Plasma Model for High-Fidelity Numerical Simulations

“…The damping rate is measured by plotting an integral of the electric field energy over time until recurrence occurs, as shown in Figure 2. The calculated rate of −0.3106 is compared to the theoretical result of −0.3066 [2,39]. Increasing the resolution of the simulation leads to the calculated damping rate converging to the theoretical value.…”

“…However, continuum kinetic models can be computationally expensive, as they solve the kinetic equation for the distribution function, which exists on up to a sixdimensional phase space while fluid and field variables exist on up to only three dimensions. Continuum kinetic models also require high resolution to resolve small phase-space features that can be present in collisionless plasmas, though previous work using higher order elements has shown success in this regard [2,29]. A Particle-In-Cell (PIC) approach can readily resolve these features and is thus a common choice for applications for collisionless problems.…”

“…As described in section 3.3, implementation of the continuum kinetic multi-species plasma model into the DG method and the computational framework in a mixed structured/unstructured formulation requires special considerations. Previous work by Reddell [2] implemented a continuum kinetic plasma model in a fully structured phase-space mesh with the DG implementation without coupling to any fluid model. This work incorporates the mixed phase-space formulation that allows coupling to the unstructured finite element spatial mesh used for the fluid plasma models.…”

“…The boundary may also be moved dynamically during a simulation using a metric determining the departure of the distribution from a Maxwellian. An example is given by Reddell [2], by defining a spatially local parameter…”

“…Some notable examples include the current sheet behavior during geomagnetic reconnection [1,2], plasma photonic crystals [3,4], field-reversed configurations (FRC's) [5][6][7], and Z-pinches [8][9][10]. Reddell [2] showed that the distribution plasma function within the thin sheath boundary was not near Maxwellian, but regions inside the reconnected region or far away from the sheath were still near Maxwellian. Tummel et al [10] demonstrated that kinetic effects can have a stabilizing effect on a flow-shear stabilized Z-pinch, while the bulk plasma may still be mostly well described by a fluid model.…”