Hello everyone,
My problem is the following. I would like to solve this set of equations:
\[ \xi^2 \frac{\partial}{\partial t} (cy_F) - \xi^3 \frac{\dot{R}}{R}
\frac{\partial}{\partial \xi} (cy_F) + \frac{1}{R} \nabla \cdot
(\xi^2 c \vec{v} y_F) = \frac{1}{R^2} \nabla \cdot (\xi^2 c \bar{D}
\nabla y_F) \]
\[ \xi^2 \frac{\partial}{\partial t} (cy_F \theta) - \xi^3
\frac{\dot{R}}{R} \frac{\partial}{\partial \xi} (cy_F \theta) +
\frac{1}{R} \nabla \cdot (\xi^2 c \vec{v} y_F \theta) = \frac{1}{R^2}
\nabla \cdot (\xi^2 c \tilde{D} y_F \nabla \theta) + \frac{1}{R^2}
\nabla \cdot (\xi^2 c \tilde{D} \theta \nabla y_F) \]
\[ \xi^2 \frac{\partial}{\partial t} (cy_F \Psi) - \xi^3
\frac{\dot{R}}{R} \frac{\partial}{\partial \xi} (cy_F \Psi) +
\frac{1}{R} \nabla \cdot (\xi^2 c \vec{v} y_F \Psi) = \frac{1}{R^2}
\nabla
\cdot (\xi^2 c \hat{D} y_F \nabla \Psi) + \frac{1}{R^2} \nabla \cdot
(\xi^2 c \hat{D} \Psi \nabla y_F) \]
I am solving for y_F, theta and Psi and the independent variables are xi
and t.
I think I have a very good idea of how to handle every term in those
equations, except for the second term. This term arises when I apply a
coordinate transformation from e.g. $y_F(r,t)$ to $y_F(\xi , t)$ where
$\xi (t)$.
After looking at the classes of various terms in the examples, I
couldn't find a way to represent $\frac{\partial}{\partial \xi}$. The
module examples.phase.impingement.mesh40x1.input has a similar term but
it uses the absolute, or magnitude of theta and this is not exactly what
I have. I have tried removing the getMag() part so that I define
theta.getGrad(), but that doesn't work, it's not the right class.
Could you please help me with that? Of course, if you need any
additional information, please ask me.
Thank you very much,
Etienne Rivard
