Multi-Material Simulation in Material Jetting#
Mathematical Model:
\[\begin{split}
\begin{align*}
&\text{Mass Transport:} \quad \frac{\partial c_i}{\partial t} + \nabla \cdot (\mathbf{v} c_i) = 0 \\
&\text{Thermal Simulation:} \quad \rho c \frac{\partial T}{\partial t} - \nabla \cdot (k \nabla T) = Q
\end{align*}
\end{split}\]
Weak Formulation:
\[\begin{split}
\begin{align*}
&\int_{\Omega} \left(\frac{\partial c_i}{\partial t} \phi_i + \nabla \cdot (\mathbf{v} c_i) \phi_i\right) \,d\Omega = 0 \\
&\int_{\Omega} \left(\rho c \frac{\partial T}{\partial t} \phi + k \nabla T \cdot \nabla \phi - Q \phi\right) \,d\Omega = 0
\end{align*}
\end{split}\]