2D Hydraulic Theory

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May 15, 2014 | Innovyze staff

InfoWorks CS/SD/RS/ICM and InfoSWMM 2D all have the capabilities to do 2D hydraulic modelling.  The 2D simulation engine used to calculate the 2D hydraulics is common to all of these Innovyze products.   A common question that gets asked is, “What 2D scheme does InfoWorks use?” and, “How are the equations solved?”. The following is an excerpt from the help page ‘Basic 2D Hydraulic Theory’ which appears in the Infoworks ICM help pages.

The 2D Engine used in Infoworks ICM is based on the procedures described in Alcrudo and Mulet-Marti (2005).  The shallow water equations (SWE), that is, the depth-average version of the Navier-Stokes equations, are used for the mathematical representation of the 2D flow. The SWE assume that the flow is predominantly horizontal and that the variation of the velocity over the vertical coordinate can be neglected. The conservative formulation of the SWE used in Infoworks ICM is described below:

Turbulence contributions are not currently modelled by Infoworks ICM.  Its effect is considered to be included in the energy loss due to the bed resistance and modelled via the Mannings n parameter.

The conservative formulation of the SWE is essential in order to preserve the basic fundamental quantities of mass and momentum. This type of formulation allows the representation of flow discontinuities and changes between gradually and rapidly varied flow.  The conservative SWE are discretised using a first-order finite volume explicit scheme.   Finite volume schemes use control volumes to represent the area of interest.  With finite volume methods the modelling domain is divided into geometric shapes over which the SWE are integrated to give equations in terms of fluxes through the control volume boundaries.  The scheme that is used to solve the SWE is based upon the Gudunov numerical scheme, with the numerical fluxes through the boundaries of the control volumes computed using the standard Roe’s approximate Riemann solver. Finite volume methods are generally considered to have a number of advantages in terms of conservativeness, geometric flexibility and conceptual simplicity.

As the scheme is an explicit solution it does not require iteration to achieve stability within defined tolerances like the 1D scheme.  Instead, for each element, the required timestep is calculated using the Courant-Friedrichs-Lewy condition in order to achieve stability, where the Courant-Friedrichs-Lewy condition is

The management of cell wetting and drying is performed using a threshold depth as a criteria to determine whether a cell is wet and the velocity is set to zero if the depth is below the threshold value (Velocity Threshold in the 2D Parameters default=0.001m).  This avoids the formation of artificially high velocities in wetting/drying areas.

Infoworks ICM uses an unstructured mesh to represent the 2D zone and this together with the scheme used allow robust simulation of rapidly varying flows (shock capturing) as well as super-critical and transcritical flows.”

The reader is also directed to the ‘Two Dimensional Flood Routing Basics’ help page for more information of the concepts of creating and running a 2D hydraulic model within the Infoworks software.

Reference: Alcrudo, F. and Mulet-Marti, J. (2005), Urban inundation models based upon the Shallow Water equations, Numerical and practical uses, in, Marrakesh,July 2005, Proceeedings of Finite Volumes for Complex Applications IV, Problems and Perspectives, Benkhaldoun, F, Ouazar, D. and Raghay, S (Eds) Hermes Science.

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Tags: 2D modeling

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