I need a solution of this eqn.
∇.(ε∇φ)=0
if there is no ε, then φ=x^2-y^2 can easily be taken as solution but I am confused as ε is present. Here ε is electrical conductivity and φ is electrical potential.
Help me please.......
I need a solution of this eqn.
∇.(ε∇φ)=0
if there is no ε, then φ=x^2-y^2 can easily be taken as solution but I am confused as ε is present. Here ε is electrical conductivity and φ is electrical potential.
Help me please.......
Actually I am trying to make simulation of flow induced by plasma actuator using PHOENICS CFD software. Here is the detailed image:
ε is a constant. In the solution domain upper part is air and bottom shaded part is dielectric material. Same equation for both domain except different dielectric constant/electrical conductivity.
for upper domain ε1 is 1 and bottom domain ε2 is 2.7. Possibly the solution should be made considering ε a function. because I have to define upper and bottom domain with 1 and 2.7 respectively.
A property of dot products is
$\displaystyle \displaystyle (c_1\mathbf{a}) \cdot (c_2\mathbf{b}) = (c_1c_2)(\mathbf{a}\cdot \mathbf{b})$.
So that means $\displaystyle \displaystyle \nabla \cdot (\varepsilon \nabla \varphi) = \varepsilon (\nabla \cdot \nabla \varphi)$.