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1.9.8
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Basilisk CFD
Adaptive Cartesian mesh PDE framework
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Go to the source code of this file.
Macros | |
| #define | rho(f) (clamp(f,0,1)*(rho1 - rho2) + rho2) |
| The density and viscosity are defined using arithmetic averages by default. | |
| #define | mu(f) (clamp(f,0,1)*(mu1 - mu2) + mu2) |
Functions | |
| void | event_defaults (void) |
| Event: defaults (i = 0) | |
| void | event_properties (void) |
| Event: properties (i++) | |
| void | event_vof (void) |
| Event: vof (i++) | |
| void | event_tracer_advection (void) |
| We set the list of interfaces back to its default value. | |
Variables | |
| scalar | f [] |
| scalar * | interfaces = {f} |
| The height functions are stored in the vector field associated with each VOF tracer. | |
| double | rho1 = 1. |
| double | mu1 = 0. |
| double | rho2 = 1. |
| double | mu2 = 0. |
| vector | alphav [] |
| Auxilliary fields are necessary to define the (variable) specific volume \(\alpha=1/\rho\) and average viscosity \(\mu\) (on faces) as well as the cell-centered density. | |
| vector | muv [] |
| scalar | rhov [] |
| static scalar * | interfaces1 = NULL |
| We overload the vof() event to transport consistently the volume fraction and the momentum of each phase. | |
The density and viscosity are defined using arithmetic averages by default.
The user can overload these definitions to use other types of averages (i.e. harmonic).
Definition at line 45 of file momentum.h.
Event: defaults (i = 0)
Boundary conditions for VOF-advected tracers usually depend on boundary conditions for the VOF field.
Event: defaults (i = 0)
Event: defaults (i = 0)
We set the default values.
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.
Event: defaults (i = 0)
Event: defaults (i = 0 )
On trees we need to ensure conservation of the tracer when refining/coarsening.
Event: defaults (i = 0)
it is an acceleration. If necessary, we allocate a new vector field to store it.
Event: defaults (i = 0)
Event: defaults (i = 0)
\[ \begin{aligned} 0 & = - \sum_k \nabla \cdot [\theta_H (hu)_k^{n + 1} + (1 - \theta_H) (hu)^n_k] \\ \frac{(hu)^{n + 1}_k - (hu)_k^n}{\Delta t} & = - \Delta tgh^{n + 1 / 2}_k (\theta_H \nabla \eta_r^{n + 1} + (1 - \theta_H) \nabla \eta_r^n) \end{aligned} \]
where \(\eta_r\) is the equivalent free-surface height (i.e. pressure) applied on the rigid lid.
Event: defaults (i = 0)
The \(w_k\) and \(\phi_k\) scalar fields are allocated and the \(w_k\) are added to the list of advected tracers.
We use (strict) minmod slope limiting for all components.
Definition at line 26 of file momentum.h.
References alpha, alphav, dimension, minmod2(), mu, muv, q, rho, rhov, theta, vector::x, and x.
We set the list of interfaces back to its default value.
Event: tracer_advection (i++)
Definition at line 138 of file momentum.h.
References interfaces, and interfaces1.
Event: vof (i++)
We split the total momentum \(q\) into its two components \(q1\) and \(q2\) associated with \(f\) and \(1 - f\) respectively.
Momentum \(q2\) is associated with \(1 - f\), so we set the inverse attribute to true. We use the same limiting for q1 and q2.
The refinement function is modified by vof_advection(). To be able to restore it, we store its value.
We associate the transport of \(q1\) and \(q2\) with \(f\) and transport all fields consistently using the VOF scheme.
We recover the total momentum.
We restore the refinement function for the total momentum.
We set the list of interfaces to NULL so that the default vof() event does nothing (otherwise we would transport \(f\) twice).
Definition at line 69 of file momentum.h.
References _i, dimension, f, free(), i, interfaces, interfaces1, list_concat(), q, q1, q2, refine(), rho, rho1, rho2, s, set_prolongation(), tracers, u, vof_advection(), vector::x, and x.
| vector alphav[] |
Auxilliary fields are necessary to define the (variable) specific volume \(\alpha=1/\rho\) and average viscosity \(\mu\) (on faces) as well as the cell-centered density.
Definition at line 22 of file momentum.h.
Referenced by event_defaults(), and event_properties().
| scalar f[] |
The interface between the fluids is tracked with a Volume-Of-Fluid method. The volume fraction in fluid 1 is \(f=1\) and \(f=0\) in fluid
Definition at line 14 of file momentum.h.
Referenced by event_properties(), and event_vof().
The height functions are stored in the vector field associated with each VOF tracer.
We will need basic functions for volume fraction computations.
They need to be updated every time the VOF field changes. For the centered Navier-Stokes solver, this means after initialisation and after VOF advection.
Note that strictly speaking this should be done for each sweep of the direction-split VOF advection, which we do not do here i.e. we use the normal at the beginning of the timestep and assume it is constant during each sweep. This seems to work fine.
Definition at line 14 of file momentum.h.
Referenced by event_tracer_advection(), and event_vof().
We overload the vof() event to transport consistently the volume fraction and the momentum of each phase.
Definition at line 66 of file momentum.h.
Referenced by event_tracer_advection(), and event_vof().
| double mu1 = 0. |
Definition at line 15 of file momentum.h.
| double mu2 = 0. |
Definition at line 15 of file momentum.h.
| vector muv[] |
Definition at line 22 of file momentum.h.
Referenced by event_defaults(), and event_properties().
| double rho1 = 1. |
Definition at line 15 of file momentum.h.
Referenced by event_acceleration(), and event_vof().
| double rho2 = 1. |
Definition at line 15 of file momentum.h.
Referenced by event_acceleration(), and event_vof().
| scalar rhov[] |
Definition at line 23 of file momentum.h.
Referenced by event_defaults(), and event_properties().
1.9.8