Improved accuracy in modelling armoured breakwaters with SPH

Transcription

1 Improved accuracy in modelling armoured breakwaters with SPH Corrado ALTOMARE 1, Alejandro J.C. Crespo 2, Benedict D. Rogers 3, Jose M. Domínguez 2, Xavier F. Gironella 1, Moncho Gómez-Gesteira 2 1 Laboratori d Enginyeria Maritima (LIM-CIIRC), Universitat Politecnica de Catalunya (UPC), Spain 2 EPHYSLAB, Universidad de Vigo, Spain 3 Modelling and Simulation Centre (MaSC), University of Manchester, UK

2 Research motivation Numerical model as useful tool in the design of coastal structures Damage Flooding HOW? FOR WHAT? 1. To help coastal physical modellers in the design of the experimental setup 2. For an early/preliminary design of coastal structures 3. To check/measure quantities difficult to assess in prototype and physical models

3 Research motivation Numerical model as useful tool in the design of coastal structures Damage Flooding Compared with other mesh-based methods for CFD, SPH simulations are computationally expensive (due to the high number of particle interactions and the low value of the time steps) Use of GPGPU (general-purpose graphics processing unit) where a GPU card is used to perform computations traditionally managed by big cluster machines with thousands of CPU cores.

4 Research motivation Numerical model as usefull tool in the design of coastal structures Damage Flooding The open-source SPH code DualSPHysics is capable of using the parallel processing power of either CPUs and GPUs and will be applied here in the numerical design of sea breakwaters

5 Research motivation Modelling the equivalent roughness of a rubble mound breakwater Represents resilience of the structure against wave run-up and overtopping events

6 Wave run-up Wave overtopping Maximum water level on the armoured slope Water flows that pass over the crest of the structure

7 Wave run-up Wave overtopping - Wave characteristics - Structure slope - Slope pattern - Block geometry - Structure permeability o tan s o

8 Wave run-up Wave overtopping - Wave characteristics - Structure slope - Slope pattern - Block geometry - Structure permeability Roughness f R rough R smooth

9 Work outline How to model the equivalent roughness numerically? f R rough R smooth

10 Research question How to model the response of the structure against run-up and overtopping events? Proper modelling of the armour layout: - Block shape and dimensions - Block interspace - Slope pattern - Slope porosity DETAILED DESCRIPTION OF THE FLOWS! Aim: obtain the equivalent surface roughness of the real case.

11 Work outline Focus on Porosity and Pattern of the armour layer Zeebrugge reference geometry (Belgium) OPTICREST (2001) and CLASH (2005) projects

12 Numerical setup 4 configurations tested f R rough R smooth Smooth equivalent slope Rough structure: 3 different patterns

13 Numerical setup f R rough R smooth Smooth equivalent slope Rough struture: 3 different patterns Regular waves attack H = 2.0 m T = 7.6 s MWL = +2.0 m surf parameter ξ 4.79 AI (p=45%) AR1 (p=51%) AR2 (p=42%)

14 Numerical setup / SPH formulation dp = 0.15m particles Time integration scheme Verlet algorithm (Verlet, 1967) Time Step Variable step that includes Courant condition and viscous effects (Monaghan & Kos 1999) Kernel Function Wendland Kernel (Wendland, 1995) Viscosity Treatment Artificial viscosity (α=0.1) (Monaghan 1992) Equation of State Tait equation (speed of sound 10 times higher than velocities in the system) Boundary Condition Dynamic Boundaries (Crespo et al. 2007) Open Periodic BC instead of lateral walls We use DBC since is convenient to model problems of wave-structure interaction. There is no need of computing normal vectors or mirror particles with this complex geometry, thus creating the initial configuration with a cloud of points is much easier using the pre-processing of DualSPHysics (GenCase by Dominguez et al th SPHERIC)

15 Numerical setup / SPH formulation dp = 0.15m particles Time integration scheme Verlet algorithm (Verlet, 1967) Time Step Variable step that includes Courant condition and viscous effects (Monaghan & Kos 1999) Kernel Function Wendland Kernel (Wendland, 1995) Viscosity Treatment Artificial viscosity (α=0.1) (Monaghan 1992) Equation of State Tait equation (speed of sound 10 times higher than velocities in the system) Boundary Condition Dynamic Boundaries (Crespo et al. 2007) Open Periodic BC instead of lateral walls The use of PBC is justified since we reduce the wave decay during its propagation

16 WITH LATERAL PERIODIC OPEN BOUNDARIES Wave1_SM No PBC With PBC Nfluid 1,982,924 1,958,742 Nboundary 457, ,353 SOLID LATERAL WALLS INSTEAD OF PBC

17 VIDEO

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20 Results

21 Results Equivalent Smooth Antifers Irregular Pattern Antifers Regular 1 Pattern Antifers Regular 2 Pattern

22 Trajectories of some particles with Antifers Irregular Pattern VIDEO

23 Results: wave height Wave heights are computed numerically for two reasons: - to prove the accuracy of the model; - to verify that we get numerically the desired waves. The values measured in the numerical flume have been used to assess the analytical run-up by means of formulae recommended in literature for regular waves.

24 Results: run-up Calculation of run-up heights: (i) first, wave heights in a set of points at the location of the structure are computed (ii) maximum wave heights are then computed for each row of points in the direction of the width of the tank, (iii) the average of all maximum wave heights are computed, (iv) finally, the maxima values are considered to get the final value of run-up.

25 VIDEO

26 Results: run-up heights for SM and AI Conf. Numerical Analytical Error (%) SM 2.78m 3.00m 7.3 AI 1.93m 1.90m 1.6

27 Results: roughness coefficient γ f,t =0.51 by measurements in Zeebrugge prototype f f,t ( 1.8)(1 f, t ) 8.2 Bruce et al. (2009) γ f =0.65 Conf. Porosity Numerical γ f Empirical γ f AI 45% AR1 51% (>45%) 0.48 <0.65 AR2 42% (<45%) 0.72 >0.65

28 Results: roughness coefficient γ f,t =0.51 by measurements in Zeebrugge prototype f f,t ( 1.8)(1 f, t ) 8.2 Bruce et al. (2009) γ f =0.65 Conf. Porosity Numerical γ f Empirical γ f AI 45% AR1 51% (>45%) 0.48 <0.65 AR2 42% (<45%) 0.72 >0.65

29 Results: roughness coefficient γ f,t =0.51 by measurements in Zeebrugge prototype f f,t ( 1.8)(1 f, t ) 8.2 Bruce et al. (2009) γ f =0.65 Conf. Porosity Numerical γ f Empirical γ f AI 45% AR1 51% (>45%) 0.48 <0.65 AR2 42% (<45%) 0.72 >0.65

30 Results: overtopping Saville. (1958) Q ( gq * o H 3 o ) 0.5 e tanh 1 hs d R s hs d s R Configuration Numerical [m 3 /s/m] Analytical [m 3 /s/m] Error (%) AI

31 Results: GPU runtimes Configuration Number of steps GPU runtime (hours) Performance (steps/second) SM 144, AI 184, AR1 190, AR2 182, The GPU card Nvidia GTX480 with 480 cores at 1.4GHz has been used as the execution device More than 2M particles and 190k steps have been simulated in less than 22 hours on my personal computer with the GPU

32 Conclusions The accuracy of SPH-based 3D model is analysed in modelling wave run-up and overtopping 4 different geometries: equivalent smooth, antifer irregular pattern, 2 antifer regular patterns with different porosity. GPU computing enables the simulation of millions of particles leading to potentially better accuracy of the numerical run-up and overtopping rates. The equivalent friction coefficient is assessed The numerical results are close to the empirical ones, showing the capability of the model to represent the phenomenon.

33 Future improvements New treatment for boundary conditions (less dissipative) A particle splitting algorithm can be used to increase particle resolution. Comparison with laboratory test results (UPV;OPTICREST-CLASH).

34 Thank you Website Free open-source DualSPHysics code: ACKNOWLEDGEMENT Xunta de Galicia under project Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas (Grupos de Referencia Competitiva) and also financed by European Regional Development Fund (FEDER).