A Review of One-Dimensional Finite-Volume Solvers for Mixed Free-Surface and Pressurized Flows

The hydraulic routing of unsteady flows in conveyance networks remains a challenging problem for water management modeling. A link-node discretization of such networks facilitates the numerical solution of the governing equations, and this approach, pioneered by EPA SWMM, has served the modeling community very well over recent decades. This approach, however, is sometimes strained for accuracy in highly unsteady flow situations, especially for rapidly filling stormwater systems, and the interest in simulating these systems is increasing in the face of evolving climate trends. Solution schemes based on finite-volume discretization, such as those originally developed for highly unsteady problems such as dam break flows, have been extended by numerous researchers to include transitions between open-channel and pressurized flows, making them suitable for application to stormwater conveyance networks.

At this writing the modeling community is fortunate to have available to it at least three one-dimensional finite volume modeling codes under active development, each of which can be readily applied to those conveyance networks expected to experience both free-surface and pressurized flow regimes. These codes are 1) the Illinois Transient Model (ITM), SWMM5+ and OpenSHAFT. These codes are similar in that they begin with a finite volume discretization, but each approaches the solution of the governing equations in a different manner. In addition, each takes a different approach to handling flow regime transitions. It is thus to be expected that the models should produce somewhat different results for highly unsteady problems. Comparing the results from multiple models, however, and attempting to understand their differences in light of the underlying assumptions, can serve to bound the uncertainty in model predictions and make the results more useful to practitioners.

This presentation will apply each of these three codes to several examples of highly unsteady conveyance networks, derived from practical applications. Output will be compared, and differences discussed with an emphasis on how they relate to differences in model formulation. The presentation will also compare and discuss model sensitivity to parameters of special importance to these solvers, such as grid cell length and acoustic wave speed. The goal is not to recommend one model code over any other, as they all have their own strengths and limitations. Instead, the presentation seeks to share experience in the application of these codes, provide guidance in parameterizing the models, and encourage their application to appropriate engineering problems.

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