Conservative discretization of the Landau collision integral

Abstract

We describe a density-, momentum-, and energy-conserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finite-element implementation.

8 pages, 1 figure, 2 tables

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Cited by in corpus (12)

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• Metriplectic Integrators for the Landau Collision Operator
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• Structure-preserving strategy for conservative simulation of relativistic nonlinear Landau--Fokker--Planck equation
• Implementation of higher-order velocity mapping between marker particles and grid in the particle-in-cell code XGC
• Multispecies structure-preserving particle discretization of the Landau collision operator
• Exascale Landau collision operator in the Cuda programming model applied to thermal quench plasmas
• Conservative Projection Between Finite Element and Particle Bases
• Relaxation to magnetohydrodynamics equilibria via collision brackets
• Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities
• A mass-energy-conserving discontinuous Galerkin scheme for the isotropic multispecies Rosenbluth--Fokker--Planck equation