Model order reduction approach to the one-dimensional collisionless closure problem

Gillot, Camille; Dif‐Pradalier, G.; Garbet, X.; Ghendrih, Philippe; Grandgirard, V.; Sarazin, Y.

doi:10.1063/5.0023407

Cited by 3 publications

(2 citation statements)

References 42 publications

(63 reference statements)

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“…Furthermore, we have observed that the electron heatflux q e builds-up in the source region at nearly constant, or even slightly positive temperature gradient. It then appears more interesting to address a non-collisional closure such that the heat-flux q is a linear combination of the lower moments [56][57][58]. The starting point are the linearized time dependent fluid equations…”

Section: Appendix Plasma-wall Self-organization Properties In the Flu...mentioning

confidence: 99%

Kinetic plasma-sheath self-organization

Munschy,

Bourne,

Dif-Pradalier

et al. 2024

Nucl. Fusion

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The interaction between a plasma and a solid surface is studied in a (1D-1V) kinetic framework using a localized particle and convective energy source. Matching the quasineutral plasma region and sheath horizon is addressed in the fluid framework with a zero heat flux closure. It highlights non-polytropic nature of the physics of parallel transport. Shortfalls of this approach compared to a reference kinetic simulation highlight the importance of the heat flux as the measure of kinetic effects. Non-collisional closure and higher moment closure are used to determine the sound velocity. Within these frameworks, no gain in the fluid predictive capability is obtained. The kinetic constraint at the sheath horizon is discussed and modified to account for conditions that are actually met in simulations, namely quasineutrality with a small but finite charge density. Analyzing the distribution functions shows that collisional transfer is mandatory to achieve steady-state self-organization on the open field lines.

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Section: Appendix Plasma-wall Self-organization Properties In the Flu...mentioning

confidence: 99%

Kinetic plasma-sheath self-organization

Munschy,

Bourne,

Dif-Pradalier

et al. 2024

Nucl. Fusion

Self Cite

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“…A conservative discretization in space and velocity of the resulting problem yields a low-rank approximation of the original dynamics. To address the problem of the fluid closure for the collisionless linear Vlasov system, an interpolatory order reduction is proposed in [13]. In the context of a particle-based discretization of kinetic plasma models, a dynamic mode decomposition (DMD) strategy has been proposed in [14] to reconstruct the electric field within an Electromagnetic particle-in-cell (EMPIC) algorithm.…”

Section: Introductionmentioning

confidence: 99%

Adaptive symplectic model order reduction of parametric particle-based Vlasov-Poisson equation

Hesthaven¹,

Pagliantini²,

Ripamonti³

2022

Preprint

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High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of parameters. In this work, we derive reducedorder models for the semi-discrete Hamiltonian system resulting from a geometric particle-in-cell approximation of the parametric Vlasov-Poisson equations. Since the problem's non-dissipative and highly nonlinear nature makes it reducible only locally in time, we adopt a nonlinear reduced basis approach where the reduced phase space evolves in time. This strategy allows a significant reduction in the number of simulated particles, but the evaluation of the nonlinear operators associated with the Vlasov-Poisson coupling remains computationally expensive. We propose a novel reduction of the nonlinear terms that combines adaptive parameter sampling and hyper-reduction techniques to address this. The proposed approach allows decoupling the operations having a cost dependent on the number of particles from those that depend on the instances of the required parameters. In particular, in each time step, the electric potential is approximated via dynamic mode decomposition (DMD) and the particle-to-grid map via a discrete empirical interpolation method (DEIM). These approximations are constructed from data obtained from a past temporal window at a few selected values of the parameters to guarantee a computationally efficient adaptation. The resulting DMD-DEIM reduced dynamical system retains the Hamiltonian structure of the full model, provides good approximations of the solution, and can be solved at a reduced computational cost.

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Adaptive symplectic model order reduction of parametric particle-based Vlasov–Poisson equation

Hesthaven,

Pagliantini,

Ripamonti

2023

Math. Comp.

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High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of parameters. In this work, we derive reduced order models for the semi-discrete Hamiltonian system resulting from a geometric particle-in-cell approximation of the parametric Vlasov–Poisson equations. Since the problem’s nondissipative and highly nonlinear nature makes it reducible only locally in time, we adopt a nonlinear reduced basis approach where the reduced phase space evolves in time. This strategy allows a significant reduction in the number of simulated particles, but the evaluation of the nonlinear operators associated with the Vlasov–Poisson coupling remains computationally expensive. We propose a novel reduction of the nonlinear terms that combines adaptive parameter sampling and hyper-reduction techniques to address this. The proposed approach allows decoupling the operations having a cost dependent on the number of particles from those that depend on the instances of the required parameters. In particular, in each time step, the electric potential is approximated via dynamic mode decomposition (DMD) and the particle-to-grid map via a discrete empirical interpolation method (DEIM). These approximations are constructed from data obtained from a past temporal window at a few selected values of the parameters to guarantee a computationally efficient adaptation. The resulting DMD-DEIM reduced dynamical system retains the Hamiltonian structure of the full model, provides good approximations of the solution, and can be solved at a reduced computational cost.

show abstract

Model order reduction approach to the one-dimensional collisionless closure problem

Cited by 3 publications

References 42 publications

Kinetic plasma-sheath self-organization

Kinetic plasma-sheath self-organization

Adaptive symplectic model order reduction of parametric particle-based Vlasov-Poisson equation

Adaptive symplectic model order reduction of parametric particle-based Vlasov–Poisson equation

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