introdução à hidrodinâmica e formulação matemática e ...25 general orientation 1....
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Introdução à Hidrodinâmica e Formulação Matemática e
numérica do Delft 3D
Bruna Arcie Polli
Objetivos
Descrição do sistema de coordenadas e formulações
matemáticas utilizadas no modelo Delft3D
Referência: manual do módulo Flow do Delft3D (Deltares, 2014)
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State-of-the-art modelling framework for hydrodynamics, water quality, ecology, waves and morphology
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Delft3D Model
Modules
Each module has its own Graphical User
Interface
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Functionality - details (1) two horizontal co-ordinate systems Cartesian co-ordinates (ξ, η) Spherical co-ordinates (λ, φ)
Delft3D: Cartesian
G
GDelft3D: Spherical
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Functionality - details (2) two vertical systems Surface and bottom following σ-layers Fixed horizontal z-layers
Follows free surface and bottom
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Grid staggering
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Equations
• Continuity, momentum and transport
Continuity
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Momentum equations in the horizontal direction
Horizontal Reynolds stresses
sources or sinks of momentum (external forces by hydraulic structures
Bruna Arcie Polli Modelagem com Delft3D
Reynolds stresses (horizontal)
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Vertical velocities
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Hydrostatic assumption
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Hydrostatic assumption
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Turbulence Model
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Structures
• Obstacles (gates, barriers, sluices, groynes, weirs, bridge piers) generally not resolved in geometry
• Hydrostatic assumption may be violated locally • Forces need to be parameterised • Modeled by quadratic energy loss term in momentum
equation
Bruna Arcie Polli Modelagem com Delft3D
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Closed boundary conditions (bed)
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Closed boundary conditions (bed)
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Closed boundary conditions (bed)
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Closed boundary conditions (surface)
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Open boundary conditions
Virtual boundary!!! (Water-water)
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Transport Equation
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Equation of State
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Shallow water solver
• implicit
• unconditionally stable
• higher order discretisation advection terms
Transport equation
• maintains strong concentration gradients
• maintains vertical stratification
Numerical implementation
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Time step limitations
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General orientation
1. identification problem, how to tackle 2. literature scan, what is known yet 3. characteristics of the study area
dominant currents, seasonal effects, morphological active physical phenomena to include, 2D or 3D
4. model boundaries availability and accuracy data tidal excursion, main flow patterns, orientation boundary
5. specifications grid, bathymetry area of interest, channels, reclamations, outfalls
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Set-up of the FLOW model-1
1. Model area and grid; Delft3D-RGFGRID
specifications from previous steps boundary fitted, orthogonal
2. Bathymetry; Delft3D-QUICKIN digitising?, different reference levels? best data (recent, high resolution) first
3. Dry points, thin dams; VISUALISATION AREA jetties, small islands, reclamations
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Set-up of the FLOW model-2
1. Open boundaries
water level, velocity, discharge? number of boundary sections forcing; time-series, Harmonic, tidal constants
2. Physical and numerical parameters roughness, wind, heat, drying & flooding parameters
3. Monitoring stations, cross-sections calibration data at inside locations
4. Sensitivity time-step accurate results?
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Set-up FLOW post processing
1. QUICKPLOT (or GPP) 2. what kind of plots, graphs
computed versus measured, predicted time-series, 2DH, 2DV, profiles, vector, iso-lines
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Calibration and verification
1. strategy, which data and periods
accuracy criteria, wet-dry, wind
2. frequency and time domain first 2DH, always time domain
3. calibration parameters bathymetry, boundary conditions, roughness
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Organisation
Files/folders • Short names • No special characters
Organisation • one folder with raw data • one folder to which scenario/simulation • one table with scenarios and names • keep it in order (not test, final-test... )
Backup / no-break • Back up of the data • Install no-breaks
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Help
Start with simple process and scenarios
Start with coarse grid in 2D and then refine and 3D Add and verify process by process Example: lake just with inflows, just with wind, just with radiation
Resolution test The results changed with refined grid? The results changed with timestep?
Compare the results with simple models Example water level/flow
Check manuals and foruns Do not force the model and be critical
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Pre-processing, RGFGRID
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Delft3D-QUICKIN, bathymetry editor
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Postprocessing, Quickplot
water level (m)
16-Mar-2014 00:00:00
x coordinate (m)
y c
oord
inate
(m
)
3.9 3.95 4 4.05 4.1 4.15 4.2
x 105
9.625
9.63
9.635
9.64
9.645
9.65
9.655x 10
6
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
time
ele
va
tio
n (
m)
float1
0h 6h 12h 18h 0h-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
Bruna Arcie Polli Modelagem com Delft3D
Exemplo: Simple channel flow
PROBLEMA
Escoamento em um canal com determinada declividade. A solução permanente é atingida, o termo de viscosidade vertical está em
balanço com o gradiente de pressão barotrópico. Para esta situação, uma solução analítica da equação das águas rasas 2D é
comparada com a solução numérica.
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Upstream
Downstream
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Equacionamento
• A solução pode ser obtida das equações de águas rasas;
• Todos os gradientes na direção horizontal e tempo são zero;
• No regime permanente o termo de viscosidade na vertical está em equilíbrio com o gradiente de pressão barotrópico.
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Dados • Comprimento do canal (x): 10000 m
• Declividade: 0.01%
• Largura (y): 1500 m
• Upstream: Q=5 m2/s (constante)
• Perfil de velocidade logarítmico
• Coeficiente de Chézy (2D)= 65 m1/2/s
• Discretização uniforme (20x3)=> 500 m x 500 m (Horizontal!!)
• Vertical: 20 camadas uniformes
• Downstream: condição de contorno => water level (forçado pela profundidade de equilíbrio)
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Dados e discretização
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x(m) m
y(m) n
Upstream
Downstream
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Resultados
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Matemática Aplicada II Universidade Federal do Paraná
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