numerical hydraulics autumn semester 2018 · 2018. 10. 31. · powerpoint presentation author:...

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Prof. Dr Markus Holzner

Author: Pascal Corso

Support: Till Zeugin

Introduction to BASEMENT

Hands-on session

Numerical Hydraulics

Autumn semester 2018

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Description

Numerical simulation software developed (and still under development) at the Laboratory of Hydraulics, Hydrology and Glaciology (VAW) of ETH Zurich

Applications

Hydrodynamics of rivers, oceans and sediment transport

• Flood prevention and safety

• River revitalization

• Water quality estimation

• Pollution treatment

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BASEMENT, what for?

Pascal Corso | Till Zeugin

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Physical models

Hydrodynamic• Saint-Venant equations (1D)• Shallow water equations (2D)• Sub-surface flow - Richard’s equations (3D)

Sediment transport• Scalar transport equation (suspended sediments)• Bedload sediment transport• Lateral transport• Gravity-induced transport

Part of “Numerical Hydraulics” course

and “Flow” lab

Part of the “River Morphodynamic

Modelling” course


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1D Saint-Venant equations (SVE)

Assumptions made to get the Saint-Venant equations:• Hydrostatic distribution of pressure• Uniform velocity over the cross-section• Horizontal water surface across the section• Small slope of the channel bottom• Steady-state resistance laws applicable for unsteady flows

Q: water discharge = uAA: cross-section area


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2D Shallow water equations (SWE)

Assumptions made to get the SWE:• Hydrostatic distribution of pressure• Small slope of the channel bottom• Steady-state resistance laws applicable for unsteady flows

h: water depthu: depth-averaged velocity in x directionv: depth-averaged velocity in y direction

τBx, τBy: bed shear stressτxx, τxy, τyx,τyy : depth-averaged viscous and turbulent stressesDxx, Dxy, Dyx,Dyy : momentum dispersion termszB: bottom elevation

Closure equations


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Computational grid and solving method

BASEchain – 1D BASEmesh – 2D


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Numerical methods for solving SVE and SWE

Finite Volume Method* based on the integral form of the flow equations set in conservative form:

Discretization of equations and solving method1. Predictor step (neglected source term)Riemann problem solver* to calculate intercell fluxes and capture flow discontinuities (wave, flood propagation)2. Corrector step• Second-order explicit time-marching scheme• Special treatments for source terms

Temporal term Flux term Source terms (bed shear stress (friction), bed slope, viscous and turbulent stresses)

*For more details on the solving methods, see BASEMENT theoretical manual available on the webpage and

lectures on Riemann solvers and finite volume method Pascal Corso | Till Zeugin

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Get familiar with BASEMENT software for 1D case with steady inflow

→ Be able to implement 1D and 2D unsteady cases, run the simulations and compare the results to answer the questions of assignment 3

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Objective of the in-class exercise

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In-class exercise - geometry

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In-class exercise

Q = 100 m3/s Q = 200 m3/s

Q = 300 m3/s Q = 400 m3/s

Q = 500 m3/s Q = 600 m3/s

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In-class exercise: running first simulations

Q = 100 m3/s Q = 200 m3/s

Q = 300 m3/s Q = 400 m3/s

Q = 500 m3/s Q = 600 m3/s

1. Perform a simulation with the assigned discharge. You have to adapt:

Flow hydrograph file

Initial conditions (try different values for “WSE_out”)

2. After how many minutes did the simulation achieve stationarity? (Compare the inflow and the outflow of the reach)


Time = 10 min

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In-class exercise

3. Plot the longitudinal profile of the water depth. What is the maximum and the minimum flow depth?(to get the water depth, subtract “z_talweg” from “wse”).


Q [m3/s]

Min depth [m]

Max depth [m]

100

200

300

400

500

600

Time = 15 min

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In-class exercise



Q [m3/s]

Min depth [m]

Max depth [m]

100 0.76 1.40

200 0.98 2.19

300 1.19 2.86

400 1.39 3.44

500 1.48 3.98

600 1.74 4.47

Q [m3/s]

Min depth [m]

Max depth [m]

100

200

300

400

500

600

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In-class exercise: water depth along the reach



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In-class exercise

4. Determine the location of the minimum and the maximum flow depth.(You can use the function “Match” in Excel =MATCH(value;array;0).This returns the index of your value in the array. In German, the function is named “Vergleich”).

Q [m3/s] Location min depth [m]

Location max depth [m]

100

200

300

400

500

600


Time = 5 min

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In-class exercise: maximum and minimum water depth

4. Determine the location of the minimum and the maximum flow depth.(You can use the function “Match” in Excel =MATCH(value;array;0).This returns the index of your value in the array. In German, the function is named “Vergleich”).



100

200

300

400

500

600



100 1065 1370

200 1070 1355

300 1065 1350

400 1060 1340

500 1060 1335

600 1055 1330


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In-class exercise: maximum and minimum water depth

4. What do you observe? How would you explain this?


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In-class exercise: wave force at maximum water depth



Euler momentum theorem (between cross-sections at 1300 m (1) and 1400 m

(2) distance from inflow)

Q [m3/s]

Δh [m]

ΔV [m/s]

ΔS [m2] F [kN]

100

200

300

400

500

600

F

Time = 10 min

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In-class exercise: wave force at maximum water depth



Euler momentum theorem (between cross-sections at 1300 m (1) and 1400 m

(2) distance from inflow)

Q [m3/s]

Δh [m]

ΔV [m/s]

ΔS [m2] F [kN]

100 -0.04 -1.18 38.73 131.9

200 0.10 -1.65 71.11 256.3

300 0.23 -1.96 99.5 364.1

400 0.34 -2.21 125.6 460.4

500 0.45 -2.41 150.1 547.7

600 0.54 -2.58 173.5 627.7

Q [m3/s]

Δh [m]

ΔV [m/s]

ΔS [m2] F [kN]

100

200

300

400

500

600

Thanks for your attention!

Questions?

numerical hydraulics autumn semester 2018 · 2018. 10. 31. · powerpoint presentation author:...

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