A coupling strategy and its software implementation for waves propaga- tion and their impact on coast Prospects Christophe Kassiotis SPH Meeting – Feb 9, 2010
Introduction Who I am ? What did I do ?. . . Ecole des Ponts ParisTech ENS Cachan EDF R&D TU-Brauncwheig University of Manchester C. Kassiotis 2 / 19 Coupling waves/SPH
Introduction Ph. D. Ecole des Ponts ParisTech ENS Cachan EDF R&D TU-Brauncwheig University of Manchester C. Kassiotis 2 / 19 Coupling waves/SPH
Introduction Now Ecole des Ponts ParisTech ENS Cachan EDF R&D TU-Brauncwheig University of Manchester C. Kassiotis 2 / 19 Coupling waves/SPH
Introduction Problem description Waves modeling from open sea to coast: Various physical models and associated software Countless applications Among important issues: extreme waves or tsunami impacts C. Kassiotis 3 / 19 Coupling waves/SPH
Introduction Problem description Waves modeling from open sea to coast: Various physical models and associated software Countless applications Among important issues: extreme waves or tsunami impacts Tsunami modeling: Generation Propagation Run-up Coupling key issues Amplitude of the flood Source: CMLA-Cachan [Dutykh, Resistance of buildings 09] C. Kassiotis 3 / 19 Coupling waves/SPH
Introduction Problem description Waves modeling from open sea to coast: Various physical models and associated software Countless applications Among important issues: extreme waves or tsunami impacts Tsunami modeling: Generation Propagation Run-up Coupling key issues Amplitude of the flood [Kassiotis, 07] Resistance of buildings C. Kassiotis 3 / 19 Coupling waves/SPH
Introduction Problem description Waves modeling from open sea to coast: Various physical models and associated software Countless applications Among important issues: extreme waves or tsunami impacts Tsunami modeling: Generation Propagation Run-up Coupling key issues Amplitude of the flood FBI, American Samoa, Sep. 09 Resistance of buildings C. Kassiotis 3 / 19 Coupling waves/SPH
Introduction Problem description Waves modeling from open sea to coast: Various physical models and associated software Countless applications Among important issues: extreme waves or tsunami impacts Tsunami modeling: Generation Propagation Run-up Coupling key issues Amplitude of the flood FBI, American Samoa, Sep. 09 Resistance of buildings C. Kassiotis 3 / 19 Coupling waves/SPH
Introduction Ph. D. results: fluid structure interaction Partitioned strategy Strong coupling Coupling FEM and FVM 292 Free-surface flow VOF g Material properties 292 Neo-Hookean structure 80 Ω f , 2 E s = 1 × 10 6 Pa, ν s = 0 , 80 ρ s = 2500 kg · m − 3 . Ω f , 1 Ω s 6 4 1 ρ f , 1 = 1000 kg / m 3 , Two-phase flow 2 9 6 2 8 ν f , 1 = 1 × 10 6 m / s, ρ f , 2 = 1 kg / m 3 , 2 2 1 0 4 1 6 4 1 6 ν f , 2 = 1 × 10 5 m / s. 4 1 C. Kassiotis 4 / 19 Coupling waves/SPH
Introduction Ph. D. results: three-dimensional dam-break problem C. Kassiotis 5 / 19 Coupling waves/SPH
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 6 / 19 Coupling waves/SPH
Outline Sub-problems 1 Waves propagation Waves sloshing on coast Coupling algorithm 2 Software implementation – Component architecture 3 C. Kassiotis 7 / 19 Coupling waves/SPH
Some existing software name licence language 2d 3d val BSQ_V2P3 (EDF R&D) Fortran � � waves funwave GPL Fortran � � � shallowWaterFoam GPL � � C++ SPH Spartacus Fortran � � � SPHysics GPL Fortran � � � C. Kassiotis 8 / 19 Coupling waves/SPH
Wave propagation Boussinesq model BSQ_V2P3 implements: Physical description wave height η horizontal velocity u reference height z α Finite difference discretization ( O (∆ x 4 )) Explicit Predictor ( O (∆ t 3 )) – Corrector ( O (∆ t 4 )) time integration scheme Stabilising filters Waves damping (sloshing) C. Kassiotis 9 / 19 Coupling waves/SPH
Wave propagation Boussinesq model – results C. Kassiotis 10 / 19 Coupling waves/SPH
Wave sloshing Using SPH A lot of open questions . . . (for me) C. Kassiotis 11 / 19 Coupling waves/SPH
Outline Sub-problems 1 Waves propagation Waves sloshing on coast Coupling algorithm 2 Software implementation – Component architecture 3 C. Kassiotis 12 / 19 Coupling waves/SPH
Coupling strategy [Narayanaswamy 09] Proposed coupling algorithm: Explicit and staggered in time Overlapping regions in space Figure from [Narayanaswamy et al 10] C. Kassiotis 13 / 19 Coupling waves/SPH
Coupling strategy [Narayanaswamy 09] 1: for n = 1 . . . n max do t = n ∆ t Bsq 2: impose wave height and velocity ( η b , v α, b ) 3: solve wave problem with ∆ t Bsq 4: get velocity on the SPH boundary: u ( x i , z i ) 5: solve SPH problem from t − ∆ t Bsq to t + ∆ t Bsq 6: 2 2 for k = 1 . . . k max do 7: t = ( n − 1 2 )∆ t Bsq + k ∆ t SPH 8: interpolate u k i and impose x k +1 = x k i + ∆ t SPH u k 9: i i solve SPH problem with time step ∆ t SPH 10: end for 11: get wave height and velocity at the reference height 12: 13: end for C. Kassiotis 14 / 19 Coupling waves/SPH
Coupling strategy [Narayanaswamy 09] 1: for n = 1 . . . n max do t = n ∆ t Bsq 2: impose wave height and velocity ( η b , v α, b ) 3: solve wave problem with ∆ t Bsq 4: get velocity on the SPH boundary: u ( x i , z i ) 5: solve SPH problem from t − ∆ t Bsq to t + ∆ t Bsq 6: 2 2 for k = 1 . . . k max do 7: t = ( n − 1 2 )∆ t Bsq + k ∆ t SPH 8: interpolate u k i and impose x k +1 = x k i + ∆ t SPH u k 9: i i solve SPH problem with time step ∆ t SPH 10: end for 11: get wave height and velocity at the reference height 12: 13: end for C. Kassiotis 14 / 19 Coupling waves/SPH
Coupling strategy [Narayanaswamy 09] 1: for n = 1 . . . n max do t = n ∆ t Bsq 2: impose wave height and velocity ( η b , v α, b ) 3: solve wave problem with ∆ t Bsq 4: get velocity on the SPH boundary: u ( x i , z i ) 5: solve SPH problem from t − ∆ t Bsq to t + ∆ t Bsq 6: 2 2 for k = 1 . . . k max do 7: t = ( n − 1 2 )∆ t Bsq + k ∆ t SPH 8: interpolate u k i and impose x k +1 = x k i + ∆ t SPH u k 9: i i solve SPH problem with time step ∆ t SPH 10: end for 11: get wave height and velocity at the reference height 12: 13: end for C. Kassiotis 14 / 19 Coupling waves/SPH
Coupling strategy [Narayanaswamy 09] 1: for n = 1 . . . n max do t = n ∆ t Bsq 2: impose wave height and velocity ( η b , v α, b ) 3: solve wave problem with ∆ t Bsq 4: get velocity on the SPH boundary: u ( x i , z i ) 5: = u α ( x i ) + ∂ x z α ∂ x hu α + ( z α − z i ) ∂ 2 x hu α + [ . . . ] solve SPH problem from t − ∆ t Bsq to t + ∆ t Bsq 6: 2 2 for k = 1 . . . k max do 7: t = ( n − 1 2 )∆ t Bsq + k ∆ t SPH 8: i and impose x k +1 interpolate u k = x k i + ∆ t SPH u k 9: i i solve SPH problem with time step ∆ t SPH 10: end for 11: get wave height and velocity at the reference height 12: C. Kassiotis 14 / 19 Coupling waves/SPH 13: end for
Coupling strategy [Narayanaswamy 09] 1: for n = 1 . . . n max do t = n ∆ t Bsq 2: impose wave height and velocity ( η b , v α, b ) 3: solve wave problem with ∆ t Bsq 4: get velocity on the SPH boundary: u ( x i , z i ) 5: solve SPH problem from t − ∆ t Bsq to t + ∆ t Bsq 6: 2 2 for k = 1 . . . k max do 7: t = ( n − 1 2 )∆ t Bsq + k ∆ t SPH 8: interpolate u k i and impose x k +1 = x k i + ∆ t SPH u k 9: i i solve SPH problem with time step ∆ t SPH 10: end for 11: get wave height and velocity at the reference height 12: 13: end for C. Kassiotis 14 / 19 Coupling waves/SPH
Coupling strategy [Narayanaswamy 09] 1: for n = 1 . . . n max do t = n ∆ t Bsq 2: impose wave height and velocity ( η b , v α, b ) 3: solve wave problem with ∆ t Bsq 4: get velocity on the SPH boundary: u ( x i , z i ) 5: solve SPH problem from t − ∆ t Bsq to t + ∆ t Bsq 6: 2 2 for k = 1 . . . k max do 7: t = ( n − 1 2 )∆ t Bsq + k ∆ t SPH 8: interpolate u k i and impose x k +1 = x k i + ∆ t SPH u k 9: i i solve SPH problem with time step ∆ t SPH 10: end for 11: get wave height and velocity at the reference height 12: 13: end for C. Kassiotis 14 / 19 Coupling waves/SPH
Coupling strategy [Narayanaswamy 09] 1: for n = 1 . . . n max do t = n ∆ t Bsq 2: impose wave height and velocity ( η b , v α, b ) 3: solve wave problem with ∆ t Bsq 4: get velocity on the SPH boundary: u ( x i , z i ) 5: solve SPH problem from t − ∆ t Bsq to t + ∆ t Bsq 6: 2 2 for k = 1 . . . k max do 7: t = ( n − 1 2 )∆ t Bsq + k ∆ t SPH 8: interpolate u k i and impose x k +1 = x k i + ∆ t SPH u k 9: i i solve SPH problem with time step ∆ t SPH 10: end for 11: get wave height and velocity at the reference height 12: 13: end for C. Kassiotis 14 / 19 Coupling waves/SPH
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