A Parallel Low-Rank Solver for the Six-Dimensional Vlasov-Maxwell Equations
arXiv:2201.03471 · doi:10.1016/j.jcp.2022.111562
Abstract
Continuum Vlasov simulations can be utilized for highly accurate modelling of fully kinetic plasmas. Great progress has been made recently regarding the applicability of the method in realistic plasma configurations. However, a reduction of the high computational cost that is inherent to fully kinetic simulations would be desirable, especially at high velocity space resolutions. For this purpose, low-rank approximations can be employed. The so far available low-rank solvers are restricted to either electrostatic systems or low dimensionality and can therefore not be applied to most space, astrophysical and fusion plasmas. In this paper we present a new parallel low-rank solver for the full six-dimensional electromagnetic Vlasov-Maxwell equations with a compression of the particle distribution function in velocity space. Special attention is paid to mass conservation and Gauss's law. The low-rank Vlasov solver is applied to standard benchmark problems of plasma turbulence and magnetic reconnection and compared to the full grid method. It yields accurate results at significantly reduced computational cost.
arXiv comment28 pages, 10 figures
References in corpus (20)
- The density-matrix renormalization group in the age of matrix product states
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- A Third-Order Semi-Discrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
- Discontinuous Galerkin algorithms for fully kinetic plasmas
- A semi-Lagrangian Vlasov solver in tensor train format
- Fully kinetic versus reduced-kinetic modelling of collisionless plasma turbulence
- Kinetic Vlasov Simulations of collisionless magnetic Reconnection
- A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation
- Dissipation measures in weakly-collisional plasmas
- Comparison of time splitting and backsubstitution methods for integrating Vlasov's equation with magnetic fields
- A low-rank projector-splitting integrator for the Vlasov--Maxwell equations with divergence correction
- Stable interpolation with isotropic and anisotropic Gaussians using Hermite generating function
- A massively parallel semi-Lagrangian solver for the six-dimensional Vlasov-Poisson equation
- A dynamical adaptive tensor method for the Vlasov-Poisson system
- Coupled Vlasov and two-fluid codes on GPUs
- ViDA: a Vlasov-DArwin solver for plasma physics at electron scales
- Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma
- Dynamo in weakly collisional nonmagnetized plasmas impeded by Landau damping of magnetic fields
- An Energy Conserving Vlasov Solver That Tolerates Coarse Velocity Space Resolutions: Simulation of MMS Reconnection Events
- Fluid Simulations of Three-Dimensional Reconnection that Capture the Lower-Hybrid Drift Instability