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mikeplus:dialog:2d_eddyviscositaet

2d Eddy Viskosität

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Menüpunkt: EPANET > Wasserzähler
Handbuch: MIKE+ 2D Overland User Guide, section 3.7: Eddy Viscosity

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Einleitung

Die Eddy Viskosität berücksichtigt näherungsweise den Effekt von kleinräumigen Turublenzen, welche im modellierten Strömungsbild nicht sichtbar sind, durch eine Erhöhung der (molekularen) Viskosität.

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Flexible Mesh

In MIKE+ steht nur mehr der modernere MIKE 21 FM-Engine zur Verfügung. Hier gilt:

"The 'old' rule of thumb for M21 'Classic' must not be followed for FM. There is no rule of thumb for FM. However, I would recommend using the Smagorinsky formulation, with a slightly higher minimum eddy viscosity value (say 0.002 m²/s), and running some sensitivity tests."

Classic grid – in MIKE+ nicht anwendbar

Früher, in den Zeiten des rasterbasierten MIKE 21-Ansatzes, auch MIKE 21 Classic grid genannt, galt folgender Satz:

"For applications with significant wetting and drying the Smagorinsky eddy viscosity formulation should not be used. This means that for the majority of MIKE FLOOD applications a constant eddy viscosity formulation should be applied. For overland flow conditions it is unlikely that eddy viscosity will have a major effect on model predictions (friction will dominate). However, for flow in and around structures, the value of eddy viscosity can have a significant effect upon predictions. Caution is advised in such cases."

Hintergrund

Eddy viscosity is used to represent sub-grid scale turbulence to provide the modeller with the opportunity to enhance or retard the natural generation of flow eddies in the solution scheme for the purpose of matching observed flow phenomena. :?: A velocity based eddy viscosity formulation is recommended in floodplain applications. :?:

Values for eddy viscosity can be calculated using a number of empirical formulas related to grid size and time step.

Selecting an eddy viscosity value that is too high will result in the modelled flow having a more uniform velocity distribution tending to distribute more of the total flow to the floodplain. Selecting an eddy viscosity value that is too low can result in significant variability in the velocity field, formation of large modelled eddies in areas of no physical manifestation of this hydraulic phenomenon and contribute to model instability.

These are the two formulations for the eddy viscosity when constant or read from a file:

1. Flux based formulation: d/dx (E dP/dx) + d/dy(E dP/dy),

where P is the flux in the x-direction and E is the eddy viscosity coefficient. Strictly speaking this formulation is only correct at a constant depth and should be applied with great care in order to avoid falsification of the flow pattern.

2. Velocity based formulation: d/dx (hE du/dx) + d/dy(hE du/dy),

where u is the velocity in the x-direction and h the water depth.

The velocity based formulation, which is more correct, is unfortunately also more difficult to implement in the numerical algorithm. This is because the system uses the fluxes as the unknown parameters and not the velocities. Therefore the velocity-based formulation is implemented by using the velocities from the previous time step. This can, however, lead to stability problems when the eddy viscosity coefficient E becomes large.

Normally the most suitable eddy viscosity formulation is the Smagorinsky model. This formulation may cause instabilities in combination with significant flooding and drying. :?: The safe and recommended approach in such applications is to choose the constant eddy viscosity description. Furthermore, the 'flux based' formulation is recommended as practical experience has shown that the velocity based formulation can potentially cause numerical instabilities. :?:

A rule of thumb an estimate of the eddy viscosity constant is: 0.02 ?x ?y / ?t [m2/s]

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mikeplus/dialog/2d_eddyviscositaet.txt · Zuletzt geändert: 2021/10/13 16:18 von 217.233.26.139