Quantum Fokker-Planck Modeling of Degenerate Electrons

TL;DR

This paper introduces a conservative numerical scheme for the quantum Fokker-Planck equation modeling degenerate electrons, ensuring accurate and conserved simulations of electron dynamics with elastic collisions.

Contribution

The paper presents a novel implicit, conservative discontinuous Galerkin scheme for the quantum Fokker-Planck equation with exact conservation properties.

Findings

The scheme accurately models electron distribution evolution.

It conserves physical quantities exactly.

Numerical tests validate the method's accuracy and robustness.

Abstract

An implicit and conservative numerical scheme is proposed for the isotropic quantum Fokker-Planck equation describing the evolution of degenerate electrons subject to elastic collisions with other electrons and ions. The electron-ion and electron-electron collision operators are discretized using a discontinuous Galerkin method, and the electron energy distribution is updated by an implicit time integration method. The numerical scheme is designed to satisfy all conservation laws exactly. Numerical tests and comparisons with other modeling approaches are shown to demonstrate the accuracy and conservation properties of the proposed method.