2D Hydrodynamic models

Introduction

Vast flood plains in global and local perspective in Bangladesh. Local flood phenomena in urban area for River Rhine in Germany. (Sources: unknown).

Hydrodynamic computations in river hydraulics use the Shallow Water Equations (SWE) to model open channel flow. The SWE are partial differential equations, being derived from the 3D Navier-Stokes equations (3D-NSE).

Remember: partial differential equations (PDEs) involve at least two variables

  • in space (boundary value problems)
  • or time (initial value problems).

The SWEs are commonly used to approximate the water depth (h) and the spatial pattern of the velocity field (u, v) and most commonly describe more than one time instance, but an entire hydrograph.

This approximation within the SWEs is a simplification, introducing time averaging and depth integration. The 2D model theory in river hydraulics assumes that vertical velocity components are negligible. Consequently, a hydrostatic pressure distribution is presumed. This simplification comes along with a reduction in computational costs afforded by the SWE approach. This is particularly important for ocean and estuary simulations, usually involving huge domains and a serious time span for a hydrodynamic simulation period, resulting in a large number of time steps. Calculations of complex flow situations such as caused by interactions with building structures or in urban areas show differences between 3D-NSE and SWE. They raise vertical velocity components that are generally not negligible.


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Hydrodynamics of Floods
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