stress.h File Reference

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Functions
void	event_defaults (void)
	Event: defaults (i = 0)
void	event_acceleration (void)
	We overload the acceleration event of the Navier–Stokes solver to add the electrohydrodynamics acceleration term.

Function Documentation

event_acceleration()

void event_acceleration

(

void

)

We overload the acceleration event of the Navier–Stokes solver to add the electrohydrodynamics acceleration term.

Event: acceleration (i++)

The electric force is the divergence of the Maxwell stress tensor \(\mathbf{M}\).

If axisymmetric cylindrical coordinates are used an additional term must be added.

To get the acceleration from the force we need to multiply by the specific volume \(\alpha\).

Definition at line 33 of file stress.h.

References _i, a, alpha, assert, av, cm, dimension, epsilon, f, fm, phi, sq(), vector::x, x, and vector::y.

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event_defaults()

void event_defaults

(

void

)

Event: defaults (i = 0)

Electrohydrodynamic stresses

The EHD force density, \(\mathbf{f}_e\), can be computed as the divergence of the Maxwell stress tensor \(\mathbf{M}\),

\[ M_{ij} = \varepsilon (E_i E_j - \frac{E^2}{2}\delta_{ij}) \]

where \(E_i\) is the \(i\)-component of the electric field, \(\mathbf{E}=-\nabla \phi\) and \(\delta_{ij}\) is the Kronecker delta.

We need to add the corresponding acceleration to the Navier–Stokes solver.

If the acceleration vector a (defined by the Navier–Stokes solver) is constant, we make it variable.

The default density field is set to unity (times the metric).

We reset the multigrid parameters to their default values.

If the viscosity is non-zero, we need to allocate the face-centered viscosity field.

We also initialize the list of tracers to be advected with the VOF function \(f\) (or its complementary function).

We set limiting.

On trees, we ensure that limiting is also applied to prolongation and refinement.

We add the interface and the density to the default display.

We switch to a pure minmod limiter by default for increased robustness.

With the MUSCL scheme we use the CFL depends on the dimension of the problem.

On trees we need to replace the default bilinear refinement/prolongation with linear so that reconstructed values also use slope limiting.

The restriction/refine attributes of the charge density are those of a tracer otherwise the conservation is not guaranteed.

By default the permittivity is unity and other quantities are zero.

Definition at line 21 of file stress.h.

References a, vector::x, and x.