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NSF Postdoctoral Research
A set of C++ code developed by Andrew E. Slaughter
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NSF Postdoctoral Research
A set of C++ code developed by Andrew E. Slaughter
|
A class for solving the volume averaged momentum equation with libMesh. More...
#include <fem/volume_average/eq_data.h>
Public Member Functions | |
| VolumeAverageEqData (EquationSystems &sys, EqVariableLinker< TransientNonlinearImplicitSystem > &velocity) | |
| Class constructor. | |
| vector< Number > | velocity (const Point &p) |
| Returns the velocity vector at a point. | |
| Number | epsilon (const Point &p) |
| A function for returning the volume fraction. | |
| Number | element_length (const Elem *elem) |
| Returns the \(\tau_1^e \) value for the advective stabilization term (Eq. 63) | |
| Number | P_alpha (const Point &p) |
| Returns the P_alpha stabilization term, Eq. 75. | |
A class for solving the volume averaged momentum equation with libMesh.
This class contains the necessary components for computing the various element and nodal parameters for the volume averaging finite element technique. All references to equations in the docmentation of this class, unless noted otherwise, it taken from Zabaras and Samanta (2004), "A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes."
| Number VolumeAverageEqData::element_length | ( | const Elem * | elem | ) |
Returns the \(\tau_1^e \) value for the advective stabilization term (Eq. 63)
\[ \tau_1^e = \min_{\vec{x}\in \Omega^e}\left [ \tau_{SUPG}, \frac{\epsilon^2(\vec{x})}{(1-\epsilon(\vec{x}))^2} \frac{Da}{Pr} \right ] */ Number tau_1(const Point& p); //! Returns the element length, Eq. 69 /*! \f[ h = 2 \left( \sum_{e=1}^{n_{en}} \left | \hat{v} \cdot \nabla N^e_{\alpha} \right | \right)^{-1} \]
| Number VolumeAverageEqData::P_alpha | ( | const Point & | p | ) |
Returns the P_alpha stabilization term, Eq. 75.
\[ P_{\alpha}^e = \frac{1}{\epsilon}\tau_1^e \vec{v}^h \cdot \nabla N^e_{\alpha} \]
1.7.6.1 
