A constrained-transport magnetohydrodynamics algorithm with near-spectral resolution

TL;DR

This paper introduces a high-order finite difference constrained-transport magnetohydrodynamics algorithm that achieves near-spectral resolution, offering faster computation, scalability, and improved magnetic divergence preservation in astrophysical simulations.

Contribution

The authors develop a finite difference constrained-transport MHD algorithm with tunable coefficients for enhanced high-wavenumber resolution, matching spectral methods' accuracy without their computational limitations.

Findings

Achieves near-spectral wavenumber resolution.

Runs faster than spectral algorithms due to finite differences.

Shows good agreement with high-order non-constrained schemes in turbulence simulations.

Abstract

Numerical simulations including magnetic fields have become important in many fields of astrophysics. Evolution of magnetic fields by the constrained transport algorithm preserves magnetic divergence to machine precision, and thus represents one preferred method for the inclusion of magnetic fields in simulations. We show that constrained transport can be implemented with volume-centered fields and hyperresistivity on a high-order finite difference stencil. Additionally, the finite-difference coefficients can be tuned to enhance high-wavenumber resolution. Similar techniques can be used for the interpolations required for dealiasing corrections at high wavenumber. Together, these measures yield an algorithm with a wavenumber resolution that approaches the theoretical maximum achieved by spectral algorithms. Because this algorithm uses finite differences instead of fast Fourier transforms, it runs faster and isn't restricted to periodic boundary conditions. Also, since the finite differences are spatially local, this algorithm is easily scalable to thousands of processors. We demonstrate that, for low-Mach-number turbulence, the results agree well with a high-order, non-constrained-transport scheme with Poisson divergence cleaning.