HydroGeoSphere/Travel Time Probability (Transport)

Output travel time statistics
HydroGeoSphere will perform descriptive statistics, following Eqs. (2.154) and (2.155): mean travel time, mode and standard deviation will be calculated at each node/element.
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Integrate production zone

 * 1) fname Name of the file which contains the list of elements that contain a mass source function and the tabulated functions. It is formatted as follows:
 * (a) nprodel Number of production elements. Read the following nprodel times:
 * i. nel, ifunc The element number and the ID (number) of the associated tabulated function.
 * (b) maxdatprod, delta_conv Size of the largest set of tabulated data which follows and the timestep size delta_conv for evaluating the convolution integral in
 * Equation 5.16. Read the following for each of the ifunc time-series:
 * i. ndata Number of data to read for the current time-series.
 * ii. time, val Time and corresponding source value.

If ifunc = 0, then $$m^*$$ corresponds to a unit and instantaneous mass input function, and thus no time-series are required in the input file.

The element nel with the maximum value of ifunc determines how many sets of time-series data must be supplied.

This option is meant to simulate a forward transport solution by means of a backward solution. It requires the problem to be backward-in-time. Integration of the backward travel time PDFs will be performed over a series of element numbers, which are input in the .np file. In a forward transport run, these elements would contain a mass source $$m^*$$. The following equation is solved at each time-step in order to simulate the output mass flux $$J_o(t)$$ resulting from a forward transport (see [Cornaton, 2003]):



J_O(t)=\int_{\Delta}\int_{0}^{t} g_t(t-u,\mathbf{x})m^*(\mathbf{x},u) \, du\,d{\Omega} $$   (Equation 5.16)

if $$m^*$$ is an arbitrary mass source function [M L−3 T−1], or



J_O(t)=\int_{\Delta} g_t(t,\mathbf{x}){\delta}(\mathbf{x}-\mathbf{x_i}) \, d{\Omega} $$   (Equation 5.17)

if $$m^*$$ is a unit and instantaneous mass input function [L−3 T−1]. $${\Delta}$$ denotes the domain of elements where $$m^*(\mathbf{x},t) \ne 0$$.


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