From Eigenfunction Expansions to CFD

in 25 years.Is it enough progress?

Iñigo J. Losada

Environmental Hydraulics Institute “IHCantabria”Universidad de Cantabria, Santander-SPAIN

Water Wave Mechanics and Coastal Engineering

Real Academia de Ingeniería

Wave transformation

Coastal structures

Developing water wave models for coastal engineering

Seaward slope geometry Vertical breakwater

High-mound breakwater

Rubble-mound breakwater

Crest

Submerged breakwater

Overwashed breakwater

Non-overtopped structure

Permeability Impervious structure

Porous breakwater

EnergyReflective sctructures

Transmitted wave energy

Dissipative structure

Composite structures

NMM

Wave transformation:

Refraction, diffraction and shoaling

(Intermediate and shallow water)

Deep water

Wave overtopping

Loads at the caisson

Incident wavesLoads at the

armour layer

Transmitted waves

Reflected wave

Seaward Leeward

Run-up / Run-down

Reflection

Transmission

Dissipation

(Ko

rten

ha

us

& O

um

era

ci, 1

99

8)

SWL

hb

hs

SWL

hb

hs

SWL

hbhs

SWL

hb

hs

h*<0.3 0.3<h*<0.6 0.9<h*<1.0 h*>1.00.6<h*<0.9

Vertical Breakwater

Low mound

Breakwater

High Mound

Composite Breakwater

Crown Walls

Rubble Mound Breakwater

Small waves Large waves

H*s<0.35 H*s>0.35

Small waves Large waves

0.1<H*s<0.2 0.2<H*s<0.6

Large waves Very large waves

0.2<H*s<0.6 H*s>0.6

Small waves

0.1<H*s<0.2

Moderate Berm Wide Berm

0.12<B*<0.4 B*>0.6

Narrow Berm

0.08<B*<0.12

5

2.5

0

7.5

0 0.2 0.4 0 0.1 0.2 0 0.1 0.2 0 0.1 0.2 t/T

Fhmax Fhq

5

2.5

0

7.5

5

2.5

0

7.5

5

2.5

0

7.5

t/Tt/Tt/T

Fhmax

Fhq

Fhmax

Fhq

Quasi-standing waveSlightly breaking

wave

Impact loads Broken waves

Fhmax

Fhq

F*h F*

hF*

h

F*h

High mound

Breakwater

Wave loads

Models based on potential flow theory

MAIN APPROACHES

Models based on Navier-Stokes equations

LagrangianEulerian

SPH

(Smoothed

Particle

Hydrodynamics)

DNS (Direct numerical Simulation)

LES (Large Eddy Simulation)

RANS/VARANS

Reynolds Averaged

Boussinesq-type

EquationsNonlinear

Shallow Water

Equations

Eigenfunction

Expansions

1990-2014

Stokes

Waves

Tony’s top ten

Source: SCOPUSWave interaction with vegetation

Torremolinos-ICCE 1988

1983Prentice Hall

World Scientific 1991

10

Multiple scale perturbation method

Parabolic equation for combined-refraction-diffraction

Crank-Nicholson scheme

REF-DIF model First course 1989/90

Tony’s top ten

Source: SCOPUS

13

14

15

16

17

Problems:

• Complex wave dispersion equation

• Newton-Raphson --Mode swapping

• Orthogonality of eigenfunctions with complex wave numbers

• Solving system of equations

18

19

20

21

Kirby

Svendsen

Kobayashi

Dalrymple

24

25

New mild-slope equation

Porous flow is included

26

27

28

Surf zone models 1-D and 2-D

Extended Boussinesq equations (Nwogu, 1993)

Fully nonlinear Boussinesq equations (Wei et al. 1995)

modified eddy viscosity model

slot technique to represent the moving shoreline and dry land

29

30

Incoming solitary wave

31

Porous

Solid

Symmetric inlet/bay connected to sea

Coupled boundary value problems

Fourier transforms + eigenfunction expansions

Helmholtz equation

System resonances to short and long wave forcings

Models based on potential flow theory

MAIN APPROACHES

Models based on Navier-Stokes equations

LagrangianEulerian

SPH

(Smoothed

Particle

Hydrodynamics)

DNS (Direct numerical Simulation)

LES (Large Eddy Simulation)

RANS/VARANS

Reynolds Averaged

Boussinesq-type

EquationsNonlinear

Shallow Water

Equations

Eigenfunction

Expansions

1999-2000

Stokes

WavesDIVORCE

36

37

38

What’s IH-2VOF ? Losada et al. (2008)

• 2-D Navier-Stokes model

• Developed at IH-Cantabria

• RANS equations

• Finite differences scheme

• Porous media flow is considered: Forcheimer model

• Turbulence model: k-Epsilon

• Free surface tracking: VOF (Volume de Fluid)

Experimental set-up

+0.8

45 m44 m 46 m 47 m

0 m

1 m

1,04

0,7

0,12

0,3

2

1

2

1

0,10,1

Dimension in meters

WG

-7

WG

-8

WG

-9

WG

-10

WG

-11

WG

-12

WG

-13

45 m44 m43 m 46 m 47 m0 m

1 m

42 m41 m40 m39 m38 m37 m36 m35 m34 m33 m32 m31 m30 m29 m28 m27 m26 m25 m24 m23 m22 m21 m20 m19 m18 m17 m

WG

-1

WG

-2

WG

-3

WG

-4

WG

-5

WG

-6

WG

-1

16 m15 m14 m13 m12 m11 m10 m9 m8 m7 m6 m5 m4 m3 m2 m1 m0 m

WG

-7

WG

-8

WG

-9

WG

-10

WG

-11

WG

-12

WG

-13

45 m44 m43 m 46 m 47 m

0 m

1 m

42 m41 m40 m39 m38 m37 m36 m

WG

-2

WG

-3

WG

-4

WG

-5

WG

-6

WG

-14

WG

-14

Free surface gauges location

45 m44 m 46 m 47 m

0 m

1 m

PG-1

PG-2

PG-3

PG-4

PG-5

PG-6

PG

-7

PG

-8

PG

-9

PG

-10

Pressure gauges locationGeometry

University of Cantabria

- Wave flume -

- 68.5 m long

- 2 m wide

- 2 m high

- Mixed piston-pendulum

type wave maker

- Active Wave Absorption

System (AWACS®)

Guanche, R., I.J. Losada and J.L. Lara. (2009). Numerical

analysis of wave loads for coastal structure stability, Ocean

engineering, ELSEVIER, 56, 543-558

Horizontal forces (FH), Vertical forces (FV), Horizontal moment (MFH) and Vertical Moment

(MFV) time evolution

Stability analysis

Irregular case: Hs=0.15m Tp=5s h=0.8m

Maximum horizontal (FH) and vertical

forces (FV)

Stability analysis: Irregular

waves

Maximum horizontal (MFH) and vertical

moments (MFV)

Irregular waves

Mean error Std deviation

Max FH 2.19% ±6.82%

Max FV -0.69% ±6.80%

Max MFH -2.11% ±7.68%

Max MFHV -0.61% ±7.01%

Iregular waves

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

Lab(kN/m)

Nu

m(k

N/m

)

Fhmax

Smax

Irregular waves

0

0.25

0.5

0.75

1

1.25

1.5

0 0.25 0.5 0.75 1 1.25 1.5

Lab(kN/m)

Nu

m(k

N/m

)

M FHmax

M FVmax

Conventional geometry Non-conventional geometry

Motivation

0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500

-8-6-4-20 2 4 6 8 101214

Run-up analysis

t(s)

Ru

n-u

p(m

)

SWL=+2.8 m.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

10

20

30

40

50

60

70

Histogram

Nu

mb

er

of

even

ts

Run-up(m)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150 0.10.20.30.40.50.60.70.80.91

Pro

bab

ilit

y

Run-up(m)

Probability distribution function

500 550 600 650 700 750 800 850

-40

-30

-20

-10

0

10

20

x(m)

y(m

)

500 550 600 650 700 750 800 850

-40

-30

-20

-10

0

10

20

x(m)

y(m

)

Overtopping analysis

0 500 1000 1500 2000 2500 3000 35000

200

400

600

t(s)

m3/m

Qmean

overtopping: 0.18204m3/s/m

0 500 1000 1500 2000 2500 3000 35000

50

100

t(s)

m3/m

Volmax

overtopping: 84.6662m3/m

0 500 1000 1500 2000 2500 3000 35000

5

10

15

t(s)

m

Layer thicknessmax

overtopping: 6m

0 500 1000 1500 2000 2500 3000 35000

5

10

15

20

t(s)

m/s

Velmax

overtopping: 6.9296m/s

500 550 600 650 700 750 800 850

-40

-30

-20

-10

0

10

20

Simulated Geometry

x(m)

y(m

)

Number of waves= 302H

s= 8.69 m; H

m0= 8.86 m

Hrms

= 6.12 m; Hmean

= 5.36 m

Hmax

= 15.84 m; time=1084.84s (Hmax

/Hs= 1.82 eta

max/H

max= 0.56 )

Tm

= 11.85 s

Ts= 16.11 s

Tp= 15.85 s

T(Hmax

)= 13.93 s

Results summary

Run-up Run-up

mean= 8.43 m

Run-up2%

= 12.18 m

Run-upmax

= 12.18 m

Overtopping

Mean overtopping discharge: 0.18204 m3/m/s

Maximum overtopping event: 84.66 m3/m

Maximum overtopping velocity: 6.92m/s

Maximum layer thickness: 6.0 m

Conventional

4.3b0.2,a

;··exp·81.9 3

s

c

sH

Rba

H

q

Franco et al. (1994) Eurotop (2008)

Plain vertical walls (d*>0.3)

300

0.04·exp 2.6· ;9.81·

c

mm

Rq

HH

Mean Overtopping discharge

Case IH2VOF Eurotop(2008) Franco et al. (1994)

Conventional 0.1820 m3/m/s 0.1917 m3m/s 0.1321 m3m/s

Non

Conventional0.1601 m3/m/s 0.1531 m3m/s 0.0894 m3m/s

48

CERC Meeting ICCE 2012-Baltimore

PROS:

• Free and open source.

• Widely used in industry.

• 3D RANS equations.

• Finite volume discretization.

• Two-phase incompressible flow.

CONS:

• No native wave generation and absorption.

• No handling of two-phase porous media flows.

Why OpenFOAM?

New solver developed on OpenFOAM

IH-FOAM solves Reynolds-averaged Navier-Stokes equations fortwo phases through finite volumes in three dimensions. It includesa large number of turbulence models like k-ε, k-ω SST or LES.

Porous media are solved by VARANS equations (Volume-Averaged/Reynolds-Averaged Navier-Stokes).

Free surface is trackedthanks to a VOF technique

Higuera, P., Lara, J.L., Losada, I.J. (2014) “Three-dimensional interaction of waves and porous coastal structures using OpenFOAM. Part I: Formulation and validation”, Coastal Engineering, Vol 83, pp 243-258

Higuera, P., Lara, J.L., Losada, I.J. (2013) “Realistic wave generation and active wave absorption for Navier-Stokes models. Application to OpenFOAM”, Coastal Engineering, Vol 71, pp 102-118

Higuera, P., Lara, J.L., Losada, I.J. (2014) “Simulating coastal engineering processeswithOpenFOAM. Coastal Engineering, Vol 71, pp 119-134

Higuera, P., Lara, J.L., Losada, I.J. (2014) “Three-dimensional interaction of waves and porous coastal structures using OpenFOAM. Part II: Application”, Coastal Engineering, Vol 83, pp 259-270

52

ICCE 2014-Seoul

IHFoam-Large scale application

• Design sea state (475 years return period)

– Hs = 6 m, Tp = 18 s, Dir: N15ºE, Tide: + 5,5 m

• Domain

– 500 x 700 x 34 m

– 10 million cells

• Simulation time

– 25 s/day@ 128 processors

N

Smallest cell 0,25 m x 0,375 m x 0,125 m

Propagation and impact of the selected wave group

DYNAMIC PRESSURE

FORCES

Here is where we are after 25 years!

Vielen Dank for these 25 years!

and

Enhorabuena por tu ingreso en la Academia

Water Wave Mechanics and Coastal

Engineering

Real Academia de Ingeniería