4780-Kuswandi - Numerical.pdf

492

NUMERICAL SIMULATION OF TSUNAMI FORCE ON BUILDING USING SMOOTHED PARTICLES

HYDRODYNAMICS

Kuswandi1*, R. Triatmadja2, and Istiarto3

1Ph.D Student, Civil and Environmental Engineering Gadjah Mada University2Civil and Environmental Engineering, Research Center for

Engineering Science Gadjah Mada University3Civil and Environmental Engineering Gadjah Mada University

Email: [email protected], [email protected], [email protected]; *Phone: +6282328275919

Abstract

Tsunami surges create catastrophic damages to buildings in considerably large coastal areas. Tsunami that surges inland eventually hit buildings with high impact and drags force that normally beyond the design capacity of the structures. Many researchers have conducted experiments regarding the interaction between tsunami surge and structure using physical modeling in laboratory and numerical simulations.

Smoothed Particles Hydrodynamics (SPH) is a numerical method in two and three dimensions of fluid dynamics equations by replacing the fluid with particles. This numerical method is a powerful tool to obtain much detail quantities such as pressures, velocities and free surface elevations around the structures during the event of tsunami attack.

This research is a part of the initial study of the first author’s PhD thesis. The research investigates the performance of three dimensional numerical simulation model using SPH to estimate hydrodynamic quantities around a structure. The results show the agreement between the numerical solution and the physical model results in term of surge speed, and tsunami surge force.

Keywords : Tsunami surge, mathematical model, hydraulic quantities, SPH

INTRODUCTION

General Background

Indonesia has been hit by tsunami many times in the last decade. The frequency of tsunami in Indonesia is increasing whilst the coastal areas have become more populated. The situation certainly increases the risk of tsunami disaster. For this reason, it is of importance to carry out more effective study to mitigate tsunami disasters.

4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta

493

One of the most important parts of tsunami mitigation is assuring that important buildings near the beach area are strong enough not to be destroyed by tsunami. Such structures may be used to protect other buildings or as vertical evacuation shelters. The destruction of such buildings may due to direct interaction or force by tsunami and indirect cause for example due to scouring. For these two cases, the problems are actually very complex where many researchers have carried out.

When Tsunami surges hit structures, the pressure, velocity and the surges height are important variables that give impact to the fluid-soil-structures interaction. Many researches on tsunami force on structures have been conducted using physical experiments as well as numerical models. The physical model approaches (for instant Triatmadja & Any Nurhasanah, 2012, Nurhasanah, 2010, Lukunprasit et.al, 2008) seems to give direct and reliable data, yet the efforts and facilities limitations may make the method not suitable for a certain research purpose.

Smoothed Particle Hydrodynamics (SPH) is a powerful numerical method that is capable to obtain detail quantities such as pressures, velocities and free surface elevations during fluid-structure interaction such as in tsunami attack.

This research is a basic research (early stage research) for PhD thesis. At this stage of research we are able to present the simulation of surge due to a dam break using SPH and its comparison with physical model results.

From the literature on SPH applications, it is apparent that high speed computer is required to carry out SPH simulation. Therefore, the present study employed a special designed computer PC of high speed specification. The PC was also supported with high capacity graphic capability to support visualization. In addition, physical model simulation was also carried out to calibrate and compare the numerical results.

LITERATURE STUDY

Theory of SPH

Smoothed Particle Hydrodynamics (SPH) is a numerical method based on integral interpolant equation (Monaghan, 2005). In SPH, the fundamental principle is to approximate any function A (r’) by

................................................................. (1)

where h is the smoothing kernel and is the weighting function or kernel.


494

This approximation, in discrete notation, leads to the following approximation of the function at a particle (interpolation point) a,

................................................................................. (2)

Where, Ab, rb are the mass and density respectively and is the weighting function or kernel

Time Step Algorithm

The time step algorithm is calculated with the relationship between pressure and density which was suggested by many as explained by Monoghan 2005. It is assumed to follow the expression

...................................................................................... (3)

where

g = 7, and ,

is the speed of sound at the

reference density

Density Filter

The Moving Least Squares (MLS) approach is given in SPH User Manual (Gesteira et al, 2010). This is the first order correction so that the linear variation of the density field and is explained below:

.................................................. (4)

The corrected kernel is evaluated as follows:

.............................................. (5)

wherethe correction vector b is given

where

With the matrix is given by

............. (6)


495

Viscosity Treatment

The artificial viscosity has been used very often due to its simplicity (Molteni, 2007). In SPH the equation of artificial viscosity can be written as

........................................... (7)

where The pressure gradient form in symmetrical and in SPH notation is expressed as :

.................................................. (8)

where Pk dan rkare pressure and density corresponding to particle k (evaluated at a or b particles) . Pab is the viscosity term :

............................................................... (9)

With

........................................................................................... (10)

Where ;

,

Adalah position and velocity of particle k (a or b),

α is free parameter.

Methodology of StudyThe research is carried out using numerical simulation based on Smoothed Particle Hydrodynamics (SPH). The results are compared with physical model results. In numerical simulation, the kernel function selected for the simulation is Quintic written by Wenland in 1995 as explained in SPH User Manual, whilst the momentum equation was that suggested and developed by Monaghan.

The physical model was prepared in Hydraulic and Hydrology laboratory, Center for Engineering Science, Universitas Gadjah Mada, Yogyakarta. A flume of 16.8 long, 0.6 wide and 0.45 deep was used to generate tsunami surge based on dam break system (Figure 1). When the gate (Figure 1) is quickly opened, a surge similar to tsunami surge on land is created depending on the initial depth of the basin. The height and speed of the surge were recorded. The surge heights were recorded using wave probes, whilst the surge speeds were measured indirectly based on surges arrival time.


496

In order to compare the surge force of the numerical and physical models, a rectangular column was installed at the end of the channel. The arrangement of the model is given in Figure 1 and Figure 2.

Figure 1. Schematic arrangement of the dam-break system

(a) (b) Figure 2. Vertical Wall Model Setup in flume (a) Front View (b) Side View


497

RESULTS AND DISCUSSION

In order to run the Smoothed Particle Hydrodynamics (SPH) of the original case 2 (Gesteira et al 2010) the kernel function was replaced with spline cubic kernel function which provide faster running speed and more realistic solution. The result of the numerical simulation using SPH is largely depend on the viscosity employed for the model. The maximum surge front speed at different viscosities are provided in Figure 3. The calibrated viscosity to achieve similarity with the experimental data is 0,009. With such viscosity, the numerical tsunami surge velocity, 2.355 m/s, matched the experimental data generated using 0.4 m basin depth.

Figure 3. Calibration viscosity vs velocity for simulation

Figure 4 & Figure 5 shows the numerical tsunami surge time series that was generated by the dam break system using SPH. The series was arranged to show the development of the surge from the beginning until the surge has been reflected by

Figure 4. Numerical tsunami surge portraits


498

the wall at the end of the flume. Figure 3 shows surge time series from t= 0 second (before the gate was opened), 0.5 s, 1.0 s, 1.5 s, 2 s, 3.0 s, 3.5 s, 4.0 s, 4.5 s, 5.0 s, 5.5 s and 6.0 s. It was observed that the surge front velocity was changing depending on the stage of surge development. It was found that the maximum surge front velocity was reached at 3.3 seconds after the gate was opened.

Figure 5. Physical model (left) and Numerical model surge (right) before and after reflection from the wall

The surge front speed was reduced almost linearly until it reached the end of the flume where it drops significantly due to reflection. Figure 6 shows the maximum surge front speed with time. After the reflection, the speed reduced substantially, since the location of maximum speed moved upstream.

Figure 6. The Surge speed from open gate for simulation


499

Figure 7 shows fluctuation water elevation front gate until the wall at the end flume which numerical and experiment result. When tsunami surge were impacted at the vertical wall that the water would reflected and the particle’s of water throw up then fall in front vertical wall.

Figure 7. The water elevation compared between SPH simulation and experiment

Figure 8 shows the distribution of pressure at a section have a maximum pressure nearly the vertical wall. The pressure value on SPH is 18.48 % larger than the experimental result, these are 3832.51 Pa (SPH) and 3234.71 Pa (experiment). The numerical results were measured at the end wall of the flume, whilst the physical model results were measured 1.8 cm in front of the end wall. Hence the two models are not exactly the same and that the physical model is expected to suffer less hydrodynamic pressure. Although we need to adjust and calibrate further the numerical model against the physical model, the present result is encouraging for the next step of our study.

Figure 8. The Distribution Pressure


500

CONCLUSION AND RECOMMENDATION

During the calibration, the viscosity value was found to be 0.009. This value affects the maximum time step used in the simulation. The surge front speed, the water level along the flume and the force on vertical wall (buildings) agree with the experimental data.

ACKNOWLEDGEMENTS

The authors would like to express their gratitude’s to General Director of Higher Education, Ministry of Education and Culture on competition grant research program 2012 and Hydraulic and Hydrology laboratory, Study Center of Engineering, University Gadjah Mada, Yogyakarta for supporting our research.

The authors have also received significant help from Dr. Arno Mayrhofer to carry out the numerical simulation.

REFERENCES

Crespo, A.J.C, Geisteira - Gomez. M, Dalrymple R.A, 2007, Validation and Accuracy to Experiments Using Different Code Compiling Option (Benchmark Test Case5)., Proceding SPHERIC 2nd International Workshop, Universidad Poltenica de Madrid, Spain

Gesteira., Rogers, Dalrymple., Crespo.,Narayanaswamy., 2010., User Guides For The SPHysics Code., https : // wiki.manchester.ac.uk /sphysics /index.php/SPHYSICS_Home_Page

Molteni , Colagrossi Colicchio ., 2007. On the use of an alternative water state Equation in SPH., Smoothed Particle Hydrodynamics European research (SPHERIC)., SPHERIC 2nd International Workshop., Universidad politécnica de madrid, spain

Monoghan, J.J, 2005, Smoothed Particle Hydrodynamics, INSTITUTE OF PHYSICS PUBLISHING, Rep. Prog. Phys. 68 (2005) 1703–1759

Triatmadja. R., and Any Nurhasanah, 2012, Tsunami Force On Buildings With Openings And Protection, Journal of Earthquake and Tsunami, Vol. 6, No.4 (17 pages),@World Scientific Publishing Company

Documents

4780-Kuswandi - Numerical.pdf