Structure preserving numerical methods for the Vlasov equation
Lukas Einkemmer
TL;DR
This paper evaluates structure-preserving semi-Lagrangian discontinuous Galerkin methods for the Vlasov-Poisson system, emphasizing invariant preservation during long-term simulations and comparing performance with cubic spline interpolation.
Contribution
It introduces and assesses a semi-Lagrangian discontinuous Galerkin method for the Vlasov-Poisson system, highlighting its invariant-preserving capabilities and performance advantages.
Findings
Effective preservation of physical invariants over long simulations
Comparable or improved accuracy relative to cubic spline interpolation
Successful application to two-stream instability simulations
Abstract
To preserve a number of physically relevant invariants is a major concern when considering long time integration of the Vlasov equation. In the present work we consider the semi-Lagrangian discontinuous Galerkin method for the Vlasov-Poisson system. We discuss the performance of this method and compare it to cubic spline interpolation, where appropriate. In addition, numerical simulations for the two-stream instability are shown.
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Taxonomy
TopicsGas Dynamics and Kinetic Theory · Computational Fluid Dynamics and Aerodynamics · Magnetic confinement fusion research