scholarly journals A CONTRIBUTION TO MAGNETIC RECONNECTION: A BOLTZMANN CORRECTION TO THE MAGNETIC INDUCTION EQUATION FOR FARADAY VORTEX TUBES

2018 ◽  
Vol 26 (1) ◽  
pp. 29
Author(s):  
Vladimir L. Borsch
Keyword(s):  
Magnetic Reconnection ◽  
Magnetic Induction ◽  
Induction Equation ◽  
Magnetic Induction Equation ◽  
Vortex Tubes

scholarly journals Stable upwind schemes for the magnetic induction equation

2009 ◽  
Vol 43 (5) ◽  
pp. 825-852 ◽  
Author(s):  
Franz G. Fuchs ◽  
Kenneth H. Karlsen ◽  
Siddharta Mishra ◽  
Nils H. Risebro
Keyword(s):  
Magnetic Induction ◽  
Upwind Schemes ◽  
Induction Equation ◽  
Magnetic Induction Equation

scholarly journals High Order Hierarchical Divergence-Free Constrained Transport H(div) Finite Element Method for Magnetic Induction Equation

2017 ◽  
Vol 10 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Wei Cai ◽  
Jun Hu ◽  
Shangyou Zhang
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Magnetic Induction ◽  
High Order ◽  
Free Condition ◽  
Induction Equation ◽  
Divergence Free ◽  
Magnetic Induction Equation ◽  
Element Method

AbstractIn this paper, we propose to use the interior functions of an hierarchical basis for high order BDMp elements to enforce the divergence-free condition of a magnetic field B approximated by the H(div)BDMp basis. The resulting constrained finite element method can be used to solve magnetic induction equation in MHD equations. The proposed procedure is based on the fact that the scalar (p–1)-th order polynomial space on each element can be decomposed as an orthogonal sum of the subspace defined by the divergence of the interior functions of the p-th order BDMp basis and the constant function. Therefore, the interior functions can be used to remove element-wise all higher order terms except the constant in the divergence error of the finite element solution of the B-field. The constant terms from each element can be then easily corrected using a first order H(div) basis globally. Numerical results for a 3-D magnetic induction equation show the effectiveness of the proposed method in enforcing divergence-free condition of the magnetic field.

Sign in / Sign up

Export Citation Format

Share Document