Open boundary conditions for SPH representing free surface flows A - - PowerPoint PPT Presentation

▶
open boundary conditions for sph representing free
SMART_READER_LITE
LIVE PREVIEW

Open boundary conditions for SPH representing free surface flows A - - PowerPoint PPT Presentation

Dec 12, 2022 146 likes •428 views

Open boundary conditions for SPH representing free surface flows A big (?) step to handle SPH-Boussinesq cou- pling Christophe Kassiotis School of MACE, University of Manchester e Paris-Est ( EDF R&D, LHSV, Universit Ecole des

slide-1
SLIDE 1

Open boundary conditions for SPH representing free surface flows

A big (?) step to handle SPH-Boussinesq cou- pling Christophe Kassiotis

School of MACE, University of Manchester LHSV, Universit´ e Paris-Est (´ EDF R&D, ´ Ecole des Ponts ParisTech, CETMEF)

SPH Meeting – June 1st, 2010

slide-2
SLIDE 2

Outline

1 Introduction & Context 2 First attempt: imposing velocity/pressure

Description Examples

3 Second attempt: boundary for SWE

Description Example: steady flow over a bump

4 Conclusion

  • C. Kassiotis

OBC for SPH 2 / 21

slide-3
SLIDE 3

Introduction

Waves model (Boussinesq, Saint-Venant) Unable to represent complex free surface (multi-connected domains) Can represent sloshing with damping

[Benoit 02, Yu 99]

Studies shows the necessity of more physical models [Duthyk 10] Sloshing representation (VOF, SPH) Waves damping (can be handled by ad-hoc treatment) Computational coast (3D computations un-reachable) Coupling is a natural choice

  • C. Kassiotis

OBC for SPH 3 / 21

slide-4
SLIDE 4

Wave propagation

Boussinesq model – results

  • C. Kassiotis

OBC for SPH 4 / 21

slide-5
SLIDE 5

Breaking wave

Using SPH model

Usual boundary condition: solid wavemaker We want to avoid it and implement Open Boundary Condition

  • C. Kassiotis

OBC for SPH 5 / 21

slide-6
SLIDE 6

Outline

1 Introduction & Context 2 First attempt: imposing velocity/pressure

Description Examples

3 Second attempt: boundary for SWE

Description Example: steady flow over a bump

4 Conclusion

  • C. Kassiotis

OBC for SPH 6 / 21

slide-7
SLIDE 7

Open boundary condition

Using a buffer zone To complete particle kernels Where we can impose pressure/velocity Handle deleting/creating particles Problems No-free surface at the boundary If other quantities should be imposed?

  • C. Kassiotis

OBC for SPH 7 / 21

slide-8
SLIDE 8

Open boundary condition

Using a buffer zone To complete particle kernels Where we can impose pressure/velocity Handle deleting/creating particles Problems No-free surface at the boundary If other quantities should be imposed? Riemman invariant

  • C. Kassiotis

OBC for SPH 7 / 21

slide-9
SLIDE 9

Open boundary condition

  • C. Kassiotis

OBC for SPH 8 / 21

slide-10
SLIDE 10

Outline

1 Introduction & Context 2 First attempt: imposing velocity/pressure

Description Examples

3 Second attempt: boundary for SWE

Description Example: steady flow over a bump

4 Conclusion

  • C. Kassiotis

OBC for SPH 9 / 21

slide-11
SLIDE 11

Open boundary condition based on shallow water equations

[Vacondio et al 10]

Shallow water equations Dtρh = −ρh∇ · v Dtv = −h∇ρh + g (∇b + Sf )

  • C. Kassiotis

OBC for SPH 10 / 21

slide-12
SLIDE 12

Open boundary condition based on shallow water equations

Shallow water equation boundary conditions Inflow v · nout < 0 Outflow v · nout > 0 Subcritical v <

  • gh

Supercritical v >

  • gh

Use Riemann invariants at OB according to local Froude number

  • C. Kassiotis

OBC for SPH 11 / 21

slide-13
SLIDE 13

Open boundary condition based on shallow water equations

Shallow water equation boundary conditions Inflow v · nout < 0 Outflow v · nout > 0 Subcritical v <

  • gh

Supercritical v >

  • gh

Use Riemann invariants at OB according to local Froude number Subcritical outflow: h is imposed v1 = vi,1 + 2√g

  • hi −

√ h

  • v3 = 0
  • C. Kassiotis

OBC for SPH 11 / 21

slide-14
SLIDE 14

Open boundary condition based on shallow water equations

Shallow water equation boundary conditions Inflow v · nout < 0 Outflow v · nout > 0 Subcritical v <

  • gh

Supercritical v >

  • gh

Use Riemann invariants at OB according to local Froude number Subcritical inflow: v is imposed h =

  • 1

2√g (vi,1 − v1) +

  • hi

2

  • C. Kassiotis

OBC for SPH 11 / 21

slide-15
SLIDE 15

Open boundary condition based on shallow water equations

Shallow water equation boundary conditions Inflow v · nout < 0 Outflow v · nout > 0 Subcritical v <

  • gh

Supercritical v >

  • gh

Use Riemann invariants at OB according to local Froude number Supercritical outflow: v1 = vi,1 h = hi

  • C. Kassiotis

OBC for SPH 11 / 21

slide-16
SLIDE 16

Open boundary condition based on shallow water equations

Shallow water equation boundary conditions Inflow v · nout < 0 Outflow v · nout > 0 Subcritical v <

  • gh

Supercritical v >

  • gh

Use Riemann invariants at OB according to local Froude number Supercritical inflow: v is imposed h is imposed

  • C. Kassiotis

OBC for SPH 11 / 21

slide-17
SLIDE 17

OBC based on shallow water equations

Compute SWE unknowns with SPH

Compute water depth using at x = (x1, x3): ρ(x1, x3) =

  • j

ρjW (x − xj)mj ρj Water for x3 ∈ [b, h] with ρ(x1, x3) > αρw Here α = 0.5 Mean velocity computed as: v1(x1) = 1 h − b h

b

v1(x1, x3)dx3

  • C. Kassiotis

OBC for SPH 12 / 21

slide-18
SLIDE 18

OBC based on shallow water equations

Compute SWE unknowns with SPH

Compute water depth using at x = (x1, x3): ρ(x1, x3) =

  • j

ρjW (x − xj)mj ρj Water for x3 ∈ [b, h] with ρ(x1, x3) > αρw Here α = 0.5 Mean velocity computed as: v1(x1) = 1 h − b h

b

v1(x1, x3)dx3 ≃ 1 h − b

h−b ∆x3

  • k=1

v1(x1, k∆x3)∆x3

  • C. Kassiotis

OBC for SPH 12 / 21

slide-19
SLIDE 19

OBC based on shallow water equations

Compute SWE unknowns with SPH

200 400 600 800 1000 1200 0.25 0.5 0.75 Density (kg.m−3) Height (m)

  • C. Kassiotis

OBC for SPH 13 / 21

slide-20
SLIDE 20

OBC based on shallow water equations

Remarks

Initialize buffer zone Generate initial state using normal SphysicGEN OBC localization and default state in obc.dat Create buffer particle Delete out of bounds particle Buffer zone behaviour Values imposed (for kernel completeness) Delete fluid particle entering buffer zone Delete and create particles Deleted particles stored in trash Generate a particle using trash if possible

  • C. Kassiotis

OBC for SPH 14 / 21

slide-21
SLIDE 21

Water over a bump

Problem description

Problem used in

[Vacondio et al, 10] to validate SPH-SWE

Fluid domain x1 ∈ [0m, 10m] Fluid bottom b(x1) =    b0

  • 1 − (x1 − 5)2

4

  • if x1 ∈ [3m, 8m]

0 elsewhere with b0 = 20cm Analytical solution Subcritical or supercritical case

  • C. Kassiotis

OBC for SPH 15 / 21

slide-22
SLIDE 22

Water over a bump

Problem description

Problem used in

[Vacondio et al, 10] to validate SPH-SWE

Fluid domain x1 ∈ [0m, 10m] Fluid bottom b(x1) =    b0

  • 1 − (x1 − 5)2

4

  • if x1 ∈ [3m, 8m]

0 elsewhere with b0 = 20cm Analytical solution Subcritical or supercritical case

  • C. Kassiotis

OBC for SPH 15 / 21

slide-23
SLIDE 23

Water over a bump

Large overview

  • C. Kassiotis

OBC for SPH 16 / 21

slide-24
SLIDE 24

Water over a bump

Zoom on inlet

  • C. Kassiotis

OBC for SPH 17 / 21

slide-25
SLIDE 25

Water over a bump

Zoom on outlet

  • C. Kassiotis

OBC for SPH 18 / 21

slide-26
SLIDE 26

Outline

1 Introduction & Context 2 First attempt: imposing velocity/pressure

Description Examples

3 Second attempt: boundary for SWE

Description Example: steady flow over a bump

4 Conclusion

  • C. Kassiotis

OBC for SPH 19 / 21

slide-27
SLIDE 27

Conclusions and Outlooks

Conclusion: Open Boundary Condition based on Shallow Water Equations Use of Riemann invariants Problems: If the flow does not verify SWE hypothesis? (open question) Automatic boundary condition switching (easy) Accurate computation of water depth (less easy) Outlook Implementing SPH component Coupling with Boussinesq solver

  • C. Kassiotis

OBC for SPH 20 / 21

slide-28
SLIDE 28

Conclusions and Outlooks

Thank you for attention

  • C. Kassiotis

OBC for SPH 21 / 21