Dirichlet boundary condition with time-dependent decay
The PR presents a Dirichlet boundary condition with time-dependent decay, TimeDecayDirichlet
. It can be used for excavation modelling.
This boundary condition imposes the initial values of the specified primary variable at the boundary nodes, scaled by a time-dependent parameter. The scaling parameter should be monotonically decreasing over time, representing progressive removal or reduction of support (e.g., during excavation). Typically, the scaling factor starts at 1 (g(0, \mathbf{x}) = 1) at the initial time and decreases to 0 (g(t_e, \mathbf{x}) = 0) at the end of the process (t_e). The value of the boundary condition is given by g(t, \mathbf{x}) (u_0(\mathbf{x}) - u_{\text{min}}) + u_{\text{min}}, where u_0(\mathbf{x}) is the initial value of the primary variable at the boundary node \mathbf{x}, and u_{\text{min}} is the user-defined lower limit of the boundary value.
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A 1×1 square domain is initialized with a temperature gradient ranging from 76.8 ^\circ\text{C} at the top to 46.9 ^\circ\text{C} at the bottom.
A time-decaying Dirichlet boundary condition is applied to the left boundary, defined by the following piecewise linear function: g(t)= \begin{cases} 1 - t/ 0.5,\quad \forall t \in [0, 0.5] \text{day},\\ 0.0,\quad \forall t> 0.5 \text{day} \end{cases}, The corresponding lower boundary temperature is set to 16.85 ^\circ\text{C}.
The temperature at the right boundary remains fixed at its initial value.
The final temperature distribution:

The temperature variations at the points on the left boundary, which is described with the time-decaying Dirichlet boundary condition, are plotted below:

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Any new feature or behaviour change was documented?