Multispecies structure-preserving particle discretization of the Landau collision operator

Zonta, Filippo; Pusztay, Joseph V.; Hirvijoki, Eero

doi:10.1063/5.0105182

Cited by 4 publications

(4 citation statements)

References 68 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is obvious by the form of 17 in relation to the entropy functional that the particle loop constitutes an O(N 2 ) computation per time step, necessitating careful handling. This is further compounded by the implicit solve necessary to compute the particle evolution at each time step, or fixed point method used in [17]. For this task, PETSc's time stepping library is used to construct a sufficiently accurate and fast solver such that we can evaluate collisions in a reasonable amount of time, which are additionally straightforward to parallelize by construction.…”

Section: Numerical Toolsmentioning

confidence: 99%

“…The final optimization to be examined is the extension of the PETSc implementation to GPUs, similar to the work performed in [17] by Zonta et al, but in the PETSc Vec GPU back end. This work is underway and similarly to the operator provided in the continuum will leverage a Kokkos [22] backend for portability requirements.…”

Section: Concluding Remarks and Future Developmentsmentioning

confidence: 99%

“…A solution to this problem was presented by Hirvijoki in [16], with a simple conservative time discretization alongside a discrete gradient time stepping scheme which are conservative in mass, momentum, and energy, as well as monotonic in entropy production. Tests of these conservative properties were additionally performed in [17] with a GPU implementation of this operator in 2 dimensions. These efforts form the necessary foundation to develop a rigorous community implementation of the particle basis Landau collision integral for the construction of, or implementation into, general Particle-in-Cell (PIC) codes with support for full geometry solvers, with potential for an implementation of the Discrete-Gradient operator.…”

Section: Introductionmentioning

confidence: 99%

“…To begin, we will reiterate the metriplectic formulation of the Vlasov-Poisson-Landau system alongside the new particle basis approach to its evaluation. We present a novel approach to evaluation of the entropy functionals via high order quadrature on implicitly defined domains [18] and compare the quality of such methods against the standard Gauss-Hermite quadratures used in [17]. Verifica-tion of the methods are demonstrated via basic tests such as thermal equilibration and isotropization of multiple species.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Conservative Projection Between Finite Element and Particle Bases

Pusztay¹,

Knepley²,

Adams³

2022

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

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.

show abstract

Section: Numerical Toolsmentioning

confidence: 99%

Section: Concluding Remarks and Future Developmentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Conservative Projection Between Finite Element and Particle Bases

Pusztay¹,

Knepley²,

Adams³

2022

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

A Particle Method for the Multispecies Landau Equation

Carrillo,

Hu,

Van Fleet

2024

Acta Appl Math

View full text Add to dashboard Cite

The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving deterministic particle method (Carrillo et al. in J. Comput. Phys. 7:100066, 2020) has been developed for the single species spatially homogeneous Landau equation. This method relies on a regularization of the Landau collision operator so that an approximate solution, which is a linear combination of Dirac delta distributions, is well-defined. Based on a weak form of the regularized Landau equation, the time dependent locations of the Dirac delta functions satisfy a system of ordinary differential equations. In this work, we extend this particle method to the multispecies case, and examine its conservation of mass, momentum, and energy, and decay of entropy properties. We show that the equilibrium distribution of the regularized multispecies Landau equation is a Maxwellian distribution, and state a critical condition on the regularization parameters that guarantees a species independent equilibrium temperature. A convergence study comparing an exact multispecies Bobylev-Krook-Wu (BKW) solution to the particle solution shows approximately 2nd order accuracy. Important physical properties such as conservation, decay of entropy, and equilibrium distribution of the particle method are demonstrated with several numerical examples.

show abstract

The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations

Bailo,

Carrillo,

2024

J. Plasma Phys.

View full text Add to dashboard Cite

We introduce an extension of the particle-in-cell method that captures the Landau collisional effects in the Vlasov–Maxwell–Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport–collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.

show abstract

Multispecies structure-preserving particle discretization of the Landau collision operator

Cited by 4 publications

References 68 publications

Conservative Projection Between Finite Element and Particle Bases

Conservative Projection Between Finite Element and Particle Bases

A Particle Method for the Multispecies Landau Equation

The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations

Contact Info

Product

Resources

About