Urban Stormwater Modeling: Is the Shock-capturing Technique More Efficient than the Shock-fitting One?

Mathurin Daynou, Ramiro Vargas and Musandji Fuamba


Actual urban stormwater numerical models used to simulate the transient flow regime can be classified into two main approaches: shock-capturing and shock-fitting models. The first approach is of models based on the assumption of free surface flow everywhere in the conduit even if the flow is pressurised. The Preissmann slot concept is used here. The second approach determines the location of the conduit pressurisation front at each step by solving a non-linear equation system based on the conservation of mass and momentum through the front. Free surface and pressurised flows are simultaneously considered.

Due to the increasing availability of numerical models, it becomes necessary to define a rigorous basis of comparison in order to determine the effectiveness of the two approaches. Two numerical models are developed and tested in this article. The first model is a shock-capturing based model which has been developed by the combination of the Saint-Venant equations and a solution technique employing the implicit finite differences method.

The second model uses either a shock-fitting technique or the equations of mass and momentum conservation to follow the front wave propagation when the flow enters into the transitional phase with a simultaneous coexistence of free-surface and pressurised flows. Both models use robust boundary conditions to ensure uniform conditions at the system limits and a common basis for comparison.

The two models are applied to a stormwater system case study designed for a 5-y return period rainfall. A comparative analysis of obtained numerical results from the two models for a 10-y, 25-y and 50-y return period reveals a few strengths and limitations of each approach. It also provides a guidance methodology to anyone who needs to make a crucial decision on which approach (or numerical method) to select when dealing with transient flows calculations into stormwater systems.

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