Second Order Godunov Schemes for 2D and 3D MHD Equations and Divergence-Free Condition

1998 ◽  
pp. 283-297
Author(s):  
Wenlong Dai ◽  
Paul R. Woodward
Keyword(s):  
Second Order ◽  
Mhd Equations ◽  
Free Condition ◽  
Divergence Free ◽  
2D And 3D

NEW ACTIONS FOR SELF-DUAL FIELDS IN 2D AND 3D

2008 ◽  
Vol 23 (30) ◽  
pp. 4829-4840 ◽  
Author(s):  
E. M. C. ABREU ◽  
A. CALIL ◽  
L. S. GRIGORIO ◽  
M. S. GUIMARAES ◽  
C. WOTZASEK
Keyword(s):  
Condensed Phase ◽  
Continuous Mapping ◽  
Order Theory ◽  
Second Order ◽  
The Self ◽  
Dual Model ◽  
2D And 3D ◽  
Chern Simons

New actions in D = 2 and D = 3 are proposed that are dual equivalent to known theories displaying well-defined chirality and helicity, respectively, along with new interpolating actions mapping continuously through the original dualities. The new chiral action in D = 2 is a second-order theory displaying the chiral constraint dynamically. In D = 3 the helicity constraint is imposed a la Siegel displaying a continuous mapping between the Maxwell–Chern–Simons and the self-dual model. It is also shown that the resulting theories introduce new versions of the Hull noton to take care of the symmetry aspects of the original models. The new interpolating formulation is then reexamined as a condensed phase for the discussion of duality under the light of the dual mechanisms — Julia–Toulouse and Higgs — establishing new interpolating actions in the dilute phase, according to these mechanisms.

scholarly journals Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

2016 ◽  
Vol 472 (2189) ◽  
pp. 20150835 ◽  
Author(s):  
Yongbo Deng ◽  
Jan G. Korvink
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Electromagnetic Waves ◽  
Three Dimensional ◽  
Free Condition ◽  
Edge Element ◽  
Divergence Free ◽  
The Magnetic Field ◽  
Element Method

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

scholarly journals On second-order, divergence-free tensors

2014 ◽  
Vol 55 (6) ◽  
pp. 062501 ◽  
Author(s):  
José Navarro
Keyword(s):  
Second Order ◽  
Divergence Free
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