Vectorial Ohm Law + Continuity Eq.
Hello Everyone, I am trying to implement with getDP a very simple Current flow simulation, between voltage drops. The equation I am using are:
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Div J = 0
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J = -Sigma*Grad V However, I am not succeeding in this task when I start using 3D domain and thus vectorial equations. My problem raises exactly with the implementation of the Galerkin method for vectors: It is not clear to me whether use J as vector (but I am having troubles with vectorial basis set BFNodeX, BFNodeY, BFNodeZ) or separate its component [Jx,Jy,Jz] and in this case which basis function to use for the weak form of the equation.
My actual guess, not working is the following formulation://div(J) =0 Galerkin { [ Dof{d jx} , {jx} ] ; In Vol_tot; Integration I1; Jacobian JVol; } Galerkin { [ Dof{d jy} , {jy} ] ; In Vol_tot; Integration I1; Jacobian JVol; } Galerkin { [ Dof{d jz} , {jz} ] ; In Vol_tot; Integration I1; Jacobian JVol; } //sigma* Grad(u) Galerkin { [ sigma[]*Dof{Grad u} , {u} ]; In Vol_tot; Integration I1; Jacobian JVol; } //+j=0 Galerkin { [Dof{jx} , {u} ]; In Vol_tot; Integration I1; Jacobian JVol; } Galerkin { [Dof{jy} , {u} ]; In Vol_tot; Integration I1; Jacobian JVol; } Galerkin { [Dof{jz} , {u} ]; In Vol_tot; Integration I1; Jacobian JVol; }
I am completely new to this software, thus I will appreciate very much any help with my problem, but eventually also more in general some explanation with this environment (in case please contact me at massimiliano.galvagno@mail.polimi.it).
Thank you! Massimiliano Galvagno