Conservative Projection Between Finite Element and Particle Bases

Abstract

The Landau collision integral is often considered the gold standard in the context of kinetic plasma simulation due to its conservative properties, despite challenges involved in its discretization. The primary challenge when implementing an efficient computation of this operator is conserving physical properties of the continuum equation when the system is discretized. Recent work has achieved continuum discretizations using the method of Finite Elements which maintain conservation of mass, momentum, and energy, but which lacks monotonic entropy production. More recently, a particle discretization has been introduced which conserves mass, momentum, and energy, but maintains the benefit of monotonic entropy production necessary for the metriplecticity of the system. We present here an implementation of the particle basis Landau collision integral in the Portable Extensible Toolkit for Scientific Computing in 2 and 3V for the construction of a full geometry solver with a novel approach to computation of the entropy functional gradients. Verification of the operator is achieved with thermal equilibration and isotropization tests. All examples are available, open source, in the PETSc repository for reproduction.

A structure-preserving particle discretisation for the Lenard–Bernstein collision operator

“…Carrillo et al (2020) and Hirvijoki (2021) used finite-sized marker particles to discretise the Landau operator. Mollén et al (2021) and Pusztay, Knepley & Adams (2022) focused on projection/interpolation techniques for computing collision operators for particles. An alternative approach is that of Tyranowski (2021), which treats the collisions as a stochastic process, effectively modelling their underlying microscopic behaviour rather than the resultant macroscopic effects modelled by various collision operators.…”