MIKE by DHI UK and Ireland Blog

Example tidal inundation model at Sutton Harbour, Plymouth using standard structures available within MIKE 21 Flexible Mesh

Introduction

The Sutton Harbour area of Plymouth is defended against tidal flooding primarily by a system of lock gates at the entrance to the inner harbour. It is understood that the defended level afforded by the lock gates is 4.03m A.O.D (although a number of openings in the parapet wall of the southern harbour wall may slightly compromise the level of defence). This example investigates the suitability of the existing defences to accommodate a 1 in 200-year tidal event plus an allowance for climate change.

Additional notes: It is assumed that all surface water outfalls into the inner harbour have been bypassed; hence, flooding from urban drainage has been ignored. No assessment of wave height has been included within this example. The aerial photograph above was obtained from the Channel Coastal Observatory Data Catalogue (see below).

LIDAR data, for use in the model, was obtained from the Channel Coastal Observatory Data Catalogue here http://www.channelcoast.org/. Downloading data and reports from the Channel Coastal Observatory Data Catalogue is currently free of charge (registration is required).

Additional notes: CCO LIDAR data was verified by comparison with EA LIDAR data and augmented by additional depth values.

Simulation of dam break flow around buildings using a high-resolution MIKE FLOOD FM (Flexible Mesh) model

Introduction

The following example is intended to augment the MIKE FLOOD Classic (SG) results presented within the forthcoming Environment Agency Science Report 'Benchmarking of 2D Hydraulic Modelling Packages'. Information on this study can currently be found in the 'Desktop Review of 2D Hydraulic Software Packages' report; available here (opens PDF document).

This dam break test has been adapted from an original benchmark test case available from the IMPACT project (IMPACT, 2004; Soares-Frazao and Zech, 2002), for which measurements from a physical laboratory model at the Civil Engineering Laboratory of the Université Catholique de Louvain (UCL) are available. The test involves a simple topography, a dam with a 1.0m wide opening, and an idealised representation of a single building downstream of the dam.


Processor type: Intel Core 2 Quad CPU Q9450
Speed: 2.66 GHz
RAM: 4.00 GB

[2] The numerical solution of the shallow water equations (2D cases) uses an approximate Riemann solver (Roe’s scheme; Roe, 1981) to calculate the convective fluxes at the interface of the triangular and/or quadrangular cells/elements. Average gradients are estimated using the approach by Jawahar and Kamath, 2000. Numerical oscillations are avoided using a second order TVD slope limiter (Van Leer limiter; Hirch, 1990 and Darwish, 2003).

Model Parameters

Model bathymetry: Triangular elements have been used to improve the definition of the building as above (quadrangular elements have been used elsewhere, at an approximate grid resolution of 0.1m, particularly to improve definition of model bathymetry along the base slopes and to refine flow through the gate opening).

Time increment (s): 0.02 (adaptive 0.001 - 0.02)
Flood and Dry: Drying depth = 0.001, Flooding depth = 0.002 & Wetting depth = 0.005
Eddy viscosity (m2/s): Smagorinsky formulation (default)
Bed resistance: Manning's M = 100

Initial conditions: Uniform depths of 0.4m upstream from the dam and 0.02m downstream from the dam.
 
Boundary conditions: Flow is contained by vertical walls at all boundaries of the model domain (only a section of the full model is presented above).

Model Results

Grid resolution (m): 38053 nodes / 38690 elements
Total simulation time (s): 149


Maximum water surface elevations reached during the simulation (m); transformed 0.05m grid resolution.


Maximum velocities reached during the simulation (m/s); transformed 0.05m grid resolution.

MIKE 21 Flow Model FM point series output locations.

Plot of water surface elevation against time for all point series output locations (m)

Plot of velocity against time for all point series output locations (m/s)

[3] Eddy viscosity: The most suitable eddy viscosity formulation for models of this type is often the Smagorinsky model but this formulation may potentially create 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 guestimate of the eddy viscosity constant is 0.02 Δx Δy / Δt [m2/s]

Model Results

Demonstration model of tidal flows around Guernsey and Sark, The Channel Islands, for renewable energy production

Introduction

The Channel Islands have one of the highest resources of tidal flow energy in the United Kingdom. This simple modelling exercise has been undertaken in order to demonstrate the functionality and capability of MIKE 21 to investigate the viability of harnessing the tidal flows around Guernsey and Sark for energy production.





Defining the Hydrodynamic Model

• A triangular element flexible mesh has been applied over the entire model domain; comprising 38679 Elements & 20405 Nodes
• An overall time step of 300 seconds has been selected. The duration of the simulation is 7 days (2016 overall time steps). The simulation period covers an arbitrary week from 03/07/2009 – 10/07/2009. as such, higher spring tides have not been considered in this example.
• The horizontal eddy viscosity type has been set to a velocity based Smagorinsky formulation with a constant value of 0.28
• The bed resistance type has been set to Manning number and a constant value of 32 m1/3/s applied
• Coriolis forcing has been set to varying in domain
• Wind forcing has not been considered

Define model domain; import shoreline data, redistributing vertices to prepare for mesh generation


Increase definition at study area


Create computational mesh; increase definition in study area


Bathymetry data; depth values extracted from MIKE C-MAP for greater accuracy at study area


Bathymetry data; ETOPO1 1-minute grid (Amante, C. and B. W. Eakins, ETOPO1 1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis, National Geophysical Data Center, NESDIS, NOAA, U.S. Department of Commerce, Boulder, CO, August 2008)


Interpolated bathymetry; water depths (study area) relative to Chart Datum [1]

[1] Datum info: Chart Datum (CD) is usually equal to LAT in the UK (e.g. see http://www.ordnancesurvey.co.uk/oswebsite/partnerships/research/publications/docs/2003/ICZMAP_GISRUK_full_dm.pdf for height integration at the coastal zone). For a global relief model, like ETOPO2v2, which has 2 arc-minute (~4 km) cell size, the differences between vertical datums are considered to be not significant, so long as they are all near Mean Sea Level (MSL). As such, a height correction should be applied to datasets relative to Chart Datum (see below).

Mean Sea Levels relative to Chart Datum


Adjusted model bathymetry; water depths relative to Mean Sea Level


Assign tidal boundary conditions to East & West boundaries; line time series generated using MIKE 21 Toolbox (prediction based on global tide model data)


West boundary

Model Results


Calibration against UKHO tidal predictions for St Peter Port over the study period; good correlation, parameters are appropriate for the purpose of this modelling exercise


Animation of tidal current velocities; The Channel


Animation of tidal current velocities; Channel Islands


Animation of tidal current velocities; Guernsey & Sark


Introduce turbine structures between Guernsey & Sark; Turbine 1 (North) & Turbine 2 (South). Assumed parameters; Turbine diameter = 16m, Drag coefficient = 0.4


Modelled turbine velocity (m/s); assumed criteria for viability > 1m/s (say 2m/s for spring tides)

The energy available from the turbines can (for example) be estimated as follows: -

P = Cp x 0.5 x ρ x A x V³

where: -

P = power generated (W)
Cp = turbine performance coefficient
ρ = water density (seawater ~ 1025 kg/m³)
A = sweep area of the turbine (m²)
V = flow velocity (m/s)

Modelled turbine force (N)


Consider the effects of renewable energy installations in Alderney Race


Introduce pier structures. Assumed parameters; Height = 100m, Diameter = 25m.

The impact of these pier structures on modelled tidal current velocities is negligible in this example.
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