Reflection-free finite volume Maxwell's solver for adaptive grids

TL;DR

This paper introduces a reflection-free finite volume Maxwell's solver for adaptive grids that maintains divergence-free magnetic fields and Gauss law, achieving high accuracy and efficiency in 1D and 2D simulations.

Contribution

The paper presents a novel non-staggered finite volume Maxwell's solver compatible with adaptive grids, preserving divergence constraints and employing high-order reconstructions.

Findings

Successfully simulates Gaussian pulse propagation in vacuum and ionized gas

Demonstrates high spatial accuracy with non-oscillatory reconstructions

Shows computational efficiency in adaptive grid implementations

Abstract

We present a non-staggered method for the Maxwell equations in adaptively refined grids. The code is based on finite volume central scheme that preserves in a discrete form both divergence-free property of magnetic field and the Gauss law. High spatial accuracy is achieved with help of non-oscillatory extrema preserving piece-wise or piece-wise-quadratic reconstructions. The semi-discrete equations are solved by implicit-explicit Runge-Kutta method. The new adaptive grid Maxwell's solver is examined based on several 1d examples, including the an propagation of a Gaussian pulse through vacuum and partially ionised gas. Two-dimensional extension is tested with a Gaussian pulse incident on dielectric disc. Additionally, we focus on testing computational accuracy and efficiency.