The tsunami run-up simulation by the particle method at city level needs to huge number of particle at least 1 billion particles. The conventional particle simulation method is not easy to solve these huge problem even on the premise of using supercomputer. Then, a new particle method ’fully explicit Incompressible SPH’ is developed that takes into consideration both calculation eﬃciency and accuracy. Finally, we demonstrate the future plan how to use our simulation resultes for a practical ’Soft’ disaster mitigation method through the evacuation education with the Virtual Reality(VR) system

Asai, Mitsuteru

Furuichi, Mikito

Nishiura, Daisuke

Ogasawara, Keita

English

UPCommons. Portal del coneixement obert de la UPC

IS - Parallel High Performance Simulation within the Framework of Particle-Based MethodsEffective and fast large sc led Tsunam  run-up analysis using explicit ISPH methodV International Conference on Particle-based Methods – Fundamentals and ApplicationsPARTICLES 2017P. Wriggers, M. Bischoff, E. Oñate, D.R.J. Owen, & T. Zohdi (Eds)PERFORMANCE OF LARGE SCALED TSUNAMI RUN-UPANALYSIS USING EXPLICIT ISPH METHODKeita Ogasawara1, Mitsuteru Asai2, Mikito Furuichi3 and Daisuke Nishiura41 Department of Civil Engineering, Graduate School of Engineering Kyushu University744 Motooka, Nishi-ku, Fukuoka , Japanogasawara@doc.kyushu-u.ac.jp2 Department of Civil Engineering, Graduate School of Engineering Kyushu University744 Motooka, Nishi-ku, Fukuoka , Japanasai@doc.kyushu-u.ac.jp3 Department of Mathematical Science and Advanced Technology,Japan Agency forMarine-Earth Science and Technology3173-25, Showa-machi, Kanazawa-ku, Yokohama, 236-0001, Japanm-furuic@jamstec.go.jp4 Department of Mathematical Science and Advanced Technology,Japan Agency forMarine-Earth Science and Technology3173-25, Showa-machi, Kanazawa-ku, Yokohama, 236-0001, Japananishiura@jamstec.go.jpKey words: stabilized EISPH, Tsunami run-up, parallel computingAbstract. The tsunami run-up simulation by the particle method at city level needs tohuge number of particle at least 1 billion particles. The conventional particle simulationmethod is not easy to solve these huge problem even on the premise of using supercom-puter. Then, a new particle method ’fully explicit Incompressible SPH’ is developed thattakes into consideration both calculation efficiency and accuracy. Finally, we demonstratethe future plan how to use our simulation resultes for a practical ’Soft’ disaster mitigationmethod through the evacuation education with the Virtual Reality(VR) system.1 IntroductionOn March 11, 2011, the huge tsunami caused by the great east Japan earthquakedevastated many infrastructures in pacific coast of north eastern Japan. Particularly, thedamage of outflow of bridge girders caused a traffic disorder and these collapse behavioursled to delay of recovery after the disaster. After 2011 tsunami, disaster prevention andmitigation techniques are actively developing in coastal infrastructures and establishing1162Keita Ogasawara, Mitsuteru Asai, Mikito Furuichi and Daisuke Nishiuraprediction method for tsunami disaster is one of the severe issues toward the next mil-lennium tsunami. After Tohoku earthquake 2011 Japan, our research group has beendeveloped a three-dimensional tsunami run-up analysis tool using the stabilized ISPH[1]which is one of the semi-implicit Lagrangian particle method. The target site of simulationis Kochi city where huge tsunami disaster is anticipated with the next big Nankai TroughEarthquake. Tsunami run-up simulation in the urban area requires high resolution atleast 2m in order to resolve the complicated tsunami flow through buildings and the otherstructures. It leads to the large scale problem, and the tsunami run-up simulation atKochi city needs to at least 1 billion particles. It is difficult to simulate the conventionalISPH method even on the premise of using supercomputer. In this research, a new parti-cle method ’fully explicit Incompressible SPH’ is developed that takes into considerationboth calculation efficiency and accuracy. Finally, we demonstrate the future plan how touse our simulation resultes for a practical ’Soft’ disaster mitigation method through theevacuation education with the Virtual Reality(VR) system.2 Analysis methodIn the past, we adopted the stabilized ISPH method, but this method is a kind ofimplicit method and it is not suitable for large scale parallel calculation. Therefore, wehave established a method corresponding to ultra large scale parallel computation byexplicitizing the stabilized ISPH method.2.1 Governing Equations of Fluid AnalysisTo solve incompressible fluid problems , independent variables, flow velocity u andpressure p, should be obtained while satisfying the conservation law of mass and momen-tum. The governing equations in the Lagrange description are given byDρDt+ ρ∇ · u = 0 (1)DuDt= −1ρ∇p+ v∇2u+ g (2)where v is the coefficient of kinetic viscosity and g is the acceleration of gravity.Based on the assumption that the density of water is constant, the mass conservationlaw eq.(1) is rewritten as∇ · u = 0 (3)Applying Eqs. (2) and (3) to particle i, we obtainDuiDt≈ − 1ρi⟨∇pi⟩+ v⟨∇2ui⟩+ gi (4)⟨∇ · u⟩ ≈ 0 (5)The symbol of ⟨·⟩ is the approximate value referring to the values of neighbor particles inthe vicinity on the basis of the concept of the SPH method.2163Keita Ogasawara, Mitsuteru Asai, Mikito Furuichi and Daisuke Nishiura2.2 ISPH MethodIn the particle method, density is calculated through the distribution of particles,therefor it leads to the problem of the conservation of volume. To solve this problem, theISPH method, in which the velocity and pressure fields of the equations of motion areseparated using the projection method to evaluate the pressure field implicitly and thevelocity field explicitly, was proposed [2, 3]. Using the projection method, the velocityand pressure fields can be separated by defining a tentative state without consideringthe pressure gradient term in the Navier-Stokes equations of motion. In this section, theprocedure for updating variables from time step n to n + 1 is explained with the aim ofapplying the projection method to the SPH method. First, the time-derivative term ineq. (2) is subjected to forward difference approximation and the intermediate velocity u∗is defined in an intermediate state to separate the velocity asDuDt=un+1 − un∆t=un+1 − u∗∆t+u∗ − un∆t(6)Among the components of acceleration after separation, the intermediate velocity u∗ isevaluated as follows assuming that the first and second terms on the right side of eq. (6)correspond to the pressure gradient term and other terms of eq. (2), respectively.u∗i − uniDt= v⟨∇2uni ⟩+ gi→ (predictor) u∗i = uni +∆t(v⟨∇2uni ⟩+ gi)(7)The velocity from the intermediate state to the next time step is updated as followsassuming that the pressure is evaluated based on an appropriate method.un+1i − u∗i∆t= −1ρ⟨∇pn+1i ⟩→ (corrector) un+1 = u∗ +∆u∗ (8)∆u∗ = −∆t(1ρ⟨∇pn+1i ⟩)(9)As shown above, two-separated processes are implemented to update the state of velocityin ISPH method. The pressure is evaluated by solving the pressure Poisson equation givenby⟨∇2pn+1i ⟩ = −ρ0∆t⟨∇ ·∆u∗i ⟩=ρ0∆t⟨∇ · u∗i ⟩ (10)3164Keita Ogasawara, Mitsuteru Asai, Mikito Furuichi and Daisuke Nishiura2.3 A Modified Source Term to Relax the Incompressible ConditionsThe original ISPH and our proposed stabilized ISPH are applied the same projectionmethod in order to split velocity and pressure updates. In the projection method, anintermediate state is defined by excluding pressure gradient term in Navier-Stokes eqn.in (11). The difference between the original ISPH and the stabilized ISPH is the sourceterm in the pressure Poisson equation (see [1]) for the detailed formulation of equations).In the SPH method, the numerical density is evaluated by counting the number ofneighbor particles. During the fluid dynamics simulation using the ISPH, the numericaldensity is changing in time. In other words, it is difficult to keep the constant numericaldensity value because of non-uniform particle distributions. Therefore, the modified sourceterm has an important role to decrease the numerical error in the numerical density value.⟨∇2pn+1i ⟩ ≈ρ0∆t⟨∇ · u∗i ⟩+ αρ0i − ⟨ρni ⟩∆t2(11)The pressure Poisson equation given by eq. (11) completely conforms to the formulationunder a velocity divergence-free condition assuming that the relaxation parameter is zero.In addition, when the density instantaneously agrees with the initial density (or thedensity is negligibly small), the pressure Poisson equation and formulation are consideredto be the same because the second term of the source term of the pressure Poisson equationis negligible. According to the formulation, the accumulated error related to the densityproduced during analysis is gradually canceled by the term of density difference, leadingto a scheme with a good conservation of volume as a result of an almost constant densityeven for a long-term calculation.2.4 Explicit pressure assessment schemeHere, the stabilized ISPH method, which utilizes a semi-implicit time integration, isconverted to an explicit version. The most time consuming part in the ISPH is the linearequation solver for the pressure Poisson eqn.. In addition, the linear equation solver isnot so easy to get faster and to get a good parallel efficient in the supercomputers. Themain purpose of the explicit version of the stabilized ISPH is to decreasing the totalcomputational time in the supercomputer environments. The idea of the totally explicitISPH method is proposed by Barcarolo[4] et al.. They just showed a couple of numericalexamples without verification and validation. Therefore, we developed a modified EISPHmethod that satisfies accuracy and stability by explicitly solving the stabilized ISPHmethod that realized long term volume storability by referring the stabilized ISPH. InEq.(11), it can be rewritten in a discrete approximation form for the left side, the followingequation is obtained.⟨∇2P n+1i ⟩ =∑jmj2ρ0rij · ∇W (rij, h)r2ij + η2(P n+1i − P n+1j ) (12)4165Keita Ogasawara, Mitsuteru Asai, Mikito Furuichi and Daisuke NishiuraWhen Equation (12) is transformed, the following equation is obtained.P n+1i =Bi +∑j AijPn+1j∑j Aij(13)For convenience of notation, the following section is used here.Aij = mj2ρ0rij · ∇W (rij, h)r2ij + η2, Bi =ρ0∆t+ αρ0i − ρni∆t2In the equation (13), assuming that the pressure of the neighboring particles, which areoriginally unknown quantities, can be approximated by the pressure of the present timeat minute time intervals from n steps to n+1 steps, Can be rewritten as follows.P n+1i =Bi +∑j AijPnj∑j Aij(14)By using the expression (14) it is possible to make an explicit pressure assessment. Theproposed method changes only the pressure evaluation in the conventional stabilized ISPHmethod, and does not need to change the other schemes. In this study, we call the abovescheme a stabilized Explicit ISPH (EISPH) method.3 Verification test3.1 Simple dam break testBy using the stabilized EISPH method, it is possible to perform highly parallel cal-culation as compared with the calculation by the stabilized ISPH method. However,verification was conducted because verification of validity about calculation accuracy wasinsufficient. The verification problem was verified with the dam break problem shown inthe Figure 1. We analyze by both EISPH method and ISPH method referred to as conven-tional method and verify the proposed method by comparing both analysis results. Otherconditions related to analysis are as shown in Table 1, and both analyzes were carriedout under the same conditions. Regarding time increment, both methods need to satisfythe CFL condition, so we decided to use the same value (0.0002 sec). However, with theEISPH method, which is a fully explicit method, the relationship between accuracy andtime increment should be investigated separately in addition to the CFL condition. Inorder to verify focusing only on the accuracy of the EISPH method, the same conditionsas the conventional method as semi-implicit method were used. The Figure. 2 shows theresult at 6000 Step, and the color means the pressure contour, indicating that it shows aqualitatively good agreement. Figure. 3 is the time history of the pressure on the red dotin Figure. 1. This result also agrees well.5166Keita Ogasawara, Mitsuteru Asai, Mikito Furuichi and Daisuke NishiuraFigure 1: dam break modelTable 1: analysis conditionsparticle diameter number of particles time increasement10mm 214932 0.0002sec/step3.2 Tsunami run-up simulation in a real cityA tsunami run-up simulation in a real city, Japan is conducted here. Figure. 4 showsthe numerical model. The analysis conditions are as shown in Table 2, and the same valueis used for time increment here as well. The color in the figure indicates the y-directionalvelocity. It also shows that this also shows a good agreement.Figure 2: result(6000Step)6167Keita Ogasawara, Mitsuteru Asai, Mikito Furuichi and Daisuke NishiuraFigure 3: time history of th pressureFigure 4: tsunami run-up area at Kochi cityTable 2: Analysis conditionsparticle diameter number of particles time increasement4m 33591333 0.05sec/step7168Keita Ogasawara, Mitsuteru Asai, Mikito Furuichi and Daisuke NishiuraFigure 5: Results in EISPH method (left figure) and ISPH method (right figure)Figure 6: Parallelization efficiency8169Keita Ogasawara, Mitsuteru Asai, Mikito Furuichi and Daisuke NishiuraFigure 7: Virtual Reality usase example3.3 Parallelization efficiencyBy explicitization, it is not necessary to solve the pressure Poisson equation, which isthe most time consuming part in the implicit version, and it is relatively easy to performmassively parallel calculations. The figure-6 is the calculation speed improvement ratein which parallel numbers are executed in 256 parallel, 512 parallel, 1024 parallel in theabove-mentioned tsunami run-up analysis, respectively. For 256 parallels to 512 parallels,91% of the ideal value shows good parallelization efficiency. In the 1024 parallel, 78% isnot bad, but it tends to decline slightly, which seems to be overpowering as the numberof parallels is excessive for this calculation.3.4 Large scale parallelism and VR visualizationBy enabling large-scale parallel computation, it is possible to calculate with resolutionof several tens of centimeters in the tsunami run-up analysis. As a result of this, itbecomes possible to accurately resolve the tsunami that moves up the block as describedabove, so that accurate calculation becomes possible, Even in visualization it makes itpossible to draw waves through the road and it has big meaning. The authors made VRvisualization and constructed a system for enlightenment etc. of the tsunami damage.Figure. 7 is a picture walking in the image with a walking controller with visualization ofVR by computing only a specific area experimentally at 50 cm resolution. It is possibleto walk not only inside the city block where the tsunami arrives but also in the VR imagelike the one on the right.4 ConclusionsIn this study, a stabilized EISPH method is proposed for the massively parallel com-putations for tsunami run-up simulation. We are trying to utilize the 3D tsunami run-upsimulation results for the tsunami evacuation education through the VR systems. The9170Keita Ogasawara, Mitsuteru Asai, Mikito Furuichi and Daisuke NishiuraVR system is composed by the head mount display and walking controller. In the future,we plan to calculate the same tsunami run-up simulation with 50 cm resolution at thesame city model.REFERENCES[1] M. Asai, A.M.Aly, Y.Sonoda, Y.Sakai, A Stabilized Incompressible SPH method byrelaxing the Density invariance condition. International Journal for Applied Mathe-matics,No. 20130011,(2012)[2] S.J.Cummins, M.Rudman, An SPH project method, Journal ComputationalPhisics,152.(2),(1990)[3] A.Khayyer, H.Gotoh, S.Shao, Corrected incompressible SPH method for accuratewater-surface tracking in breaking waves, Coastal Engineering,55, 236–250,(2008)[4] D.A.Barcarolo, A.le Touze, F. de Vuyst, VALIDATION OF A NEW FULLY-EXPLICIT INCOMPRESSIBLE SMOOTHED PARTICLE HYDRODYNAMICSMETHOD. Blucher Mechanical Engineering Proceedings, vol.1,num.1,(2014)10171

Performance of large scaled tsunami run-up analysis using explicit ISPH method

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Performance of large scaled tsunami run-up analysis using explicit ISPH method

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