introdução à hidrodinâmica e formulação matemática e ...25 general orientation 1....

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)

2

Bruna Arcie Polli Modelagem com Delft3D

3

State-of-the-art modelling framework for hydrodynamics, water quality, ecology, waves and morphology


4

Delft3D Model

Modules

Each module has its own Graphical User

Interface


5

Functionality - details (1) two horizontal co-ordinate systems Cartesian co-ordinates (ξ, η) Spherical co-ordinates (λ, φ)

Delft3D: Cartesian

G

GDelft3D: Spherical


6

Functionality - details (2) two vertical systems Surface and bottom following σ-layers Fixed horizontal z-layers

Follows free surface and bottom


7

Grid staggering


8

Equations

• Continuity, momentum and transport

Continuity


9

Momentum equations in the horizontal direction

Horizontal Reynolds stresses

sources or sinks of momentum (external forces by hydraulic structures


Reynolds stresses (horizontal)

10


11

Vertical velocities


12

Hydrostatic assumption


13

Hydrostatic assumption


14

Turbulence Model


15

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


16

Closed boundary conditions (bed)


17



18



19

Closed boundary conditions (surface)


20

Open boundary conditions

Virtual boundary!!! (Water-water)


21

Transport Equation


22

Equation of State


23

Shallow water solver

• implicit

• unconditionally stable

• higher order discretisation advection terms

Transport equation

• maintains strong concentration gradients

• maintains vertical stratification

Numerical implementation


24

Time step limitations


25

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


26

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


27

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?


28

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


29

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


30

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


31

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


32

Pre-processing, RGFGRID


33

Delft3D-QUICKIN, bathymetry editor


34

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


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.

36

Upstream

Downstream


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.

37


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)

38


Dados e discretização

39

x(m) m

y(m) n

Upstream

Downstream


Resultados

40

Matemática Aplicada II Universidade Federal do Paraná

introdução à hidrodinâmica e formulação matemática e ...25 general orientation 1....

Documents