# Structure-preserving strategy for conservative simulation of relativistic nonlinear Landau--Fokker--Planck equation

## TL;DR

This paper introduces a structure-preserving numerical strategy for the relativistic Landau--Fokker--Planck equation that maintains its fundamental symmetries, enabling accurate mass, momentum, and energy conservation in simulations.

## Contribution

The paper presents a novel simulation method that preserves the intrinsic symmetries of the Beliaev--Budker kernel, ensuring physical conservation laws without artificial constraints.

## Key findings

- Conservation of mass, momentum, and energy achieved in simulations.
- Symmetry preservation improves the physical accuracy of relativistic plasma modeling.
- Method demonstrates robustness and fidelity in relativistic nonlinear Landau--Fokker--Planck simulations.

## Abstract

Mathematical symmetries of the Beliaev--Budker kernel are the most important structure of the relativistic Landau--Fokker--Planck equation. By preserving the beautiful symmetries, a mass-momentum-energy-conserving simulation has been demonstrated without any artificial constraints.