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iMOD User Manual version 4.4 (html)


12.35Timestep

Just a small nodal spacing is desirable, one would like to use small time steps to obtain an accurate solution as well. A good order-of-magnitude is to estimate the critical time step \(\Delta t_c\) with a formulae given by de Marsily (1986). For a homogeneous and isotropic aquifer \(\Delta t_c\) can be estimated by:

\begin{align*} \Delta t_c=S \frac {\left ( \Delta x \times \Delta y \right )^2}{4T} \end{align*}

whereby \(\Delta x\) and \(\Delta y\) are the cell sizes of the model (m), \(S\) (-) is the porosity values and \(T\) is the transmissivity value (m\(^2\)/day). The result of the equation is given in the following figure:

pictures/runfile/critical_timestep.png

Figure 12.23: Estimated critical time step (y-axis) for a porosity of \(S=0.15\) and different values for transmissivity (x-axis) and cell sizes (coloured lines)