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In the scope of the College of Arts and Science project: “Coulee Cleanway: Modelling and Analysis of the English Coulee Physiochemical Environment, UND Campus, Grand Forks”, a mathematical model attempting to describe the transportation of dissolved species within the English Coulee was developed based on “Tanks in Series”. By dividing the channel into discrete regions, a governing system of equations derived from conservation of mass equations and well-mixed assumptions is used to describe the spatial and temporal changes in concentration. The resulting system of differential equations was solved by a Runge-Kutta 4 numerical method, which allowed for the addition of probabilistic elements. Using the quick computation time of the numerical method, input parameters were selected from distributions of likely values and repeatedly ran, generating end-state distributions which could be used to determine likely outcomes. In applying the model to the English Coulee, incomplete sampling data from a Spring 2017 US Masters project was utilized in the model, with reasonable values chosen for unsampled parameters. The model was not able to be fully utilized owing to a lack of sampling information. Future work is suggested to obtain more sampling data, and create a more sophisticated model.

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Grand Forks, ND


English Coulee, Model, Modelling, Tanks, Mathematics, Numerical Simulation, Contaminant Transport




Presented at the Spring 2018 Undergraduate Showcase Grand Forks, ND, May 3, 2018.

Mathematical Modelling of English Coulee: Tanks in Series

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Mathematics Commons