Digital Hydraulics Simulation in Mathematica on Sudden Expansion Flows

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In this work, we offer readers the ability to numerically simulate flow through a sudden expansion themselves. We choose to study the sudden expansion due to its prevalence in engineered and natural water distribution networks (i.e., pipes and rivers, respectively). The simulation is written in the Wolfram Language, also known as Mathematica. The symbolic nature of this programming language enables readers to implement physical theory directly, resulting in a highly readable numerical flow solver; a stark contrast with commonplace commercial flow solvers, which operate like “black box” technologies, and low-level programming languages, which require an advanced level of syntax knowledge and programming proficiency. Upon completion of this laboratory exercise, users should be able to: (i) describe the main principles underpinning the numerical simulation of non-linear models, (ii) apply numerical models to investigate the accuracy of simplified analytical models, (iii) demonstrate a beginner-level understanding of Mathematica and, more broadly, symbolic coding environments, (ii) and most generally, (iv) understand the proper context for physical and numerical experimentation. The novelty of this work is attributed to the fact that no such simulation tool is detailed and provided in the literature for readers to utilize and alter at their discretion.

This work was developed and undertaken in collaboration with my co-authors, Dr. Anil Ganti (A.G.), and Dr. Zbigniew Kabala (Z.J.K), my master’s advisor. Author contributions are as follows: conceptualization, Z.J.K.; methodology, A.H.F, A.G. and Z.J.K.; software, A.H.F and A.G.; validation, A.H.F, A.G. and Z.J.K.; formal analysis, A.H.F; investigation, A.H.F, A.G. and Z.J.K.; resources, Z.J.K; data curation, A.H.F, A.G. and Z.J.K.; writing—original draft preparation, A.H.F and Z.J.K.; writing—review and editing, A.H.F, A.G. and Z.J.K.; visualization, A.H.F.; supervision, Z.J.K.; project administration, A.H.F and Z.J.K.

Partial funding for this project has been received from Duke University Undergraduate Program Enhancement Fund (UPEF) grant 399-000226.





Frechette, August (2023). Digital Hydraulics Simulation in Mathematica on Sudden Expansion Flows. Master's thesis, Duke University. Retrieved from


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