CFD Online Discussion Forums - one-way-coupled magnetohydrodynamics with transient magnetic fields

Quote:

Originally Posted by Jonas Holdeman (Post 454273)

I am not sure what you are asking. Do you mean adding a Lorentz force term to the fluid equations for specified magnetic fields? By one-way do you mean the magnetic field affects the fluid but the fluid does not affect the magnetic field?

Hi Jonas,

yes i mean the addition of an lorentz-force-term to the Navier-Stokes-Equations.
At this time i'm using quasi-static approximation inside a solver:

$\nabla \cdot \underline{u}=\nabla \cdot \underline{B}_0=0$

$\frac{\partial \underline{u}}{\partial t} +\left(\underline{u} \cdot \nabla\right) \underline{u} = -\frac{1}{\varrho}\nabla p + \nu \Delta \underline{u} + \underline{g} + \frac{1}{\varrho}\underline{j}\times\underline{B}_0$

$\underline{j} = \sigma\left(-\nabla\psi+\underline{u}\times\underline{B}_0\right)$

$\nabla^2\psi = \nabla \cdot \left(\underline{u}\times \underline{B}_0\right)$

This is maintained if the magnetic reynolds number $Re_{m}<<1$ . The magnetic fields reads:

. But i don't have the possibility to describe time-dependent magnetic fields.

In an two-way-coupling i have a time variation due to the coupling of velocity and magnetic field. Therefore

:

$\nabla \cdot \underline{u}=0$

$\frac{\partial \underline{u}}{\partial t} +\left(\underline{u} \cdot \nabla\right) \underline{u} = -\frac{1}{\varrho}\nabla p + \nu \Delta \underline{u} + \underline{g} -\frac{1}{2\varrho\mu}\nabla B^2 +\left(\frac{\underline{B}}{\varrho\mu}\cdot\nabla\right)\underline{B}$

$\frac{\partial\underline{B}}{\partial t} + \left(\underline{u}\cdot\nabla\right) \underline{B} = \left(\underline{B}\cdot\nabla\right) \underline{u} + \frac{1}{\sigma\mu} \Delta \underline{B}$

$\nabla \cdot \underline{B} = 0$

Now i want a time-varying magnetic field

or $B=B_0(\underline{x},t)$ . This means rotating, travelling or pulsating magnetic fields without two-way-coupling.
Maybe i don't understand it right. So please can you explain why two-way-coupling is necessary if the initial magnetic fields become time-dependant and the induced magnetic fields will be neglected.

Best regards :),

Christoph