An improved divergence-free-condition compensated method for solving incompressible flows on collocated grids

2018 ◽  
Vol 162 ◽  
pp. 39-54 ◽  
Author(s):  
Pao-Hsiung Chiu
Keyword(s):  
Incompressible Flows ◽  
Free Condition ◽  
Divergence Free ◽  
Collocated Grids

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 Divergence-free condition in transport simulation

2016 ◽  
Vol 344 (9) ◽  
pp. 642-648 ◽  
Author(s):  
Adrien Berchet ◽  
Anthony Beaudoin ◽  
Serge Huberson
Keyword(s):  
Free Condition ◽  
Transport Simulation ◽  
Divergence Free
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