2012/06/30 by Terrence S. Tricco, Daniel J. Price · 4 citations
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Astrophysics and Star Formation Studies #Classical mechanics #Dissipation #Divergence (linguistics) #Fluid Dynamics Simulations and Interactions #Hamiltonian (control theory) #Magnetic field #Magnetohydrodynamics #Mathematical analysis #Mathematical optimization #Mathematics #Nabla symbol #Physics #Quantum mechanics #Sigma #Solar and Space Plasma Dynamics #astro-ph.GA #astro-ph.IM #astro-ph.SR #physics.comp-ph
paper · pdf · doi:10.1016/j.jcp.2012.06.039
28 pages, 25 figures, accepted to J. Comput. Phys. Movies at http://www.youtube.com/playlist?list=PL215D649FD0BDA466 v2: fixed inverted figs 1,4,6, and several color bars
arxiv created 2012/07/10 · openalex publication_date 2012/07/18 · arxiv updated 2012/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a constrained formulation of Dedner et al's hyperbolic/parabolic divergence cleaning scheme for enforcing the ∇ B = 0 constraint in Smoothed Particle Magnetohydrodynamics (SPMHD) simulations. The constraint we impose is that energy removed must either be conserved or dissipated, such that the scheme is guaranteed to decrease the overall magnetic energy. This is shown to require use of conjugate numerical operators for evaluating ∇ B and ∇ψ in the SPMHD cleaning equations. The resulting scheme is shown to be stable at density jumps and free boundaries, in contrast to an earlier implementation by Price & Monaghan (2005). Optimal values of the damping parameter are found to be σ = 0.2-0.3 in 2D and σ = 0.8-1.2 in 3D. With these parameters, our constrained Hamiltonian formulation is found to provide an effective means of enforcing the divergence constraint in SPMHD, typically maintaining average values of h |∇ B| / |B| to 0.1-1%, up to an order of magnitude better than artificial resistivity without the associated dissipation in the physical field. Furthermore, when applied to realistic, 3D simulations we find an improvement of up to two orders of magnitude in momentum conservation with a corresponding improvement in numerical stability at essentially zero additional computational expense.