Vector potential-based MHD solver for non-periodic flows using Fourier continuation expansions

TL;DR

This paper introduces a high-order Fourier continuation spectral method for simulating non-periodic MHD flows, accurately enforcing divergence-free magnetic fields and accommodating various boundary conditions with minimal overhead.

Contribution

It presents a novel vector potential-based MHD solver using Fourier continuation expansions for non-periodic flows, enabling accurate boundary condition enforcement and efficient Poisson equation solutions.

Findings

Method achieves high accuracy in non-periodic MHD simulations.

Convergence improves with higher Reynolds and Hartmann numbers.

Boundary conditions are effectively enforced in complex flow scenarios.

Abstract

A high-order method to evolve in time electromagnetic and velocity fields in conducting fluids with non-periodic boundaries is presented. The method has a small overhead compared with fast FFT-based pseudospectral methods in periodic domains. It uses the magnetic vector potential formulation for accurately enforcing the null divergence of the magnetic field, and allowing for different boundary conditions including perfectly conducting walls or vacuum surroundings, two cases relevant for many astrophysical, geophysical, and industrial flows. A spectral Fourier continuation method is used to accurately represent all fields and their spatial derivatives, allowing also for efficient solution of Poisson equations with different boundaries. A study of conducting flows at different Reynolds and Hartmann numbers, and with different boundary conditions, is presented to study convergence of the method and the accuracy of the solenoidal and boundary conditions.