tension.h File Reference

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Functions
void	event_end_timestep (void)
	Event: end_timestep (i++)

Function Documentation

event_end_timestep()

void event_end_timestep

(

void

)

Event: end_timestep (i++)

Surface tension effects for the compressible solver

This module incorporates surface tension effects in the compressible solver. Unlike momentum, which is defined for the averaged mixture, the energy is defined separately for both phases. For that reason, we need to reconstruct the pressure of each phase from the averaged pressure obtained from the Helmholtz–Poisson equation.

To reconstruct \(p_1\) and \(p_2\) from the averaged pressure \(p\), we interpret the averaged pressure as

\[p = f p_1 + (1-f) p_2\]

Using the Laplace equation

\[p_2 - p_1 = -\sigma \kappa + [[\mu n \cdot \tau \cdot n]]\]

we can solve the system of the two equations for \(p_1\) and \(p_2\)

\[ p_1 = p + (1 - f) \sigma \kappa - (1-f) [[\mu n \cdot \tau \cdot n]]\]

\[ p_2 = p - f \sigma \kappa + f [[\mu n \cdot \tau \cdot n]]\]

The flux terms depending on pressure entering into the conservative total energy equation are

\[\nabla \cdot (u p_1) = \nabla \cdot (u p) + \nabla \cdot (u (1-f) \sigma \kappa) - \nabla \cdot (u (1-f) [[\mu n \cdot \tau \cdot n]])\]

\[\nabla \cdot (u p_2) = \nabla \cdot (u p) - \nabla \cdot (u f \sigma \kappa) + \nabla \cdot (u f [[\mu n \cdot \tau \cdot n]])\]

In this module we only introduce the correction due to surface tension.

Here we just introduce the correction due to the surface tension contribution to the pressure jump.

Definition at line 29 of file tension.h.

References _i, cm, curvature(), dimension, dt, f, uf, vector::x, and x.

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