Year: 2025
Type: article
Abstract: We propose a class of high order globally divergence-free spectraldiscontinuous Galerkin (DG) method for ideal magnetohydrodynamic (MHD) equations and resistive MHD equations on cylindrical coordinates (r, ϕ, z).Because the particular physical flows are toroidal symmetry or slow changes in the toroidal direction, the Fourier spectral method is adopted in the ϕ-direction and DG approximation is applied in the (r, z) plane.In particular, to satisfy the divergence-free property on cylindrical coordinates, we deform the induction equation and define the magnetic field components at interfaces.Moreover, employing a set of specially designed constraint-preserving schemes and magnetic field reconstruction techniques, we construct a general framework of the globally divergence-free spectral-DG method up to arbitrarily high order.Numerical experiments verify the robustness and efficacy of our methods.
Authors: Yuchang Liu, Yan Jiang, Mengping Zhang
Institution: University of Science and Technology of China
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: bronze
Awards: G2348142770, G774765340
OpenAlex ID: W4409424602