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International Journal of Mechanics and Materials in Design

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20-02-2017

An augmented incompressible material point method for modeling liquid sloshing problems

Authors: Fan Zhang, Xiong Zhang, Yan Liu

Published in: International Journal of Mechanics and Materials in Design | Issue 1/2018

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Abstract

The incompressible material point method was proposed for modeling the free surface flow problems based on the operator splitting technique which decouples the solution of the velocity and the pressure in our previous work. To further model the coupling problems between the incompressible fluid and the moving irregular solid bodies, an augmented incompressible material point method is proposed in this paper based on the energy minimization form of operator splitting technique. The interaction between the fluid and the solid is taken into account via the work done by the fluid pressure on the solid bodies. By minimizing the total work done by the fluid pressure, volume-weighted pressure Poisson equations are obtained. The proposed method is validated with liquid sloshing in a rectangular tank subjected to various base-excitations, and is then used to study the optimal height of baffles mounted on the bottom of the tank to mitigate the sloshing wave.

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Batty, C., Bertails, F., Bridson, R.: A fast variational framework for accurate solid-fluid coupling. In: ACM Transactions on Graphics (TOG), vol. 26, p. 100. ACM (2007)

Burghardt, J., Leavy, B., Guilkey, J., Xue, Z., Brannon, R.: Application of Uintah-MPM to shaped charge jet penetration of aluminum. In: IOP Conference Series: Materials Science and Engineering, vol. 10, p. 012223. IOP Publishing (2010)

Calderer, R., Zhu, L., Gibson, R., Masud, A.: Residual-based turbulence models and arbitrary Lagrangian–Eulerian framework for free surface flows. Math. Model. Methods Appl Sci. 25(12), 2287–2317 (2015)MathSciNetCrossRefMATH

Chen, B.F., Nokes, R.: Time-independent finite difference analysis of fully non-linear and viscous fluid sloshing in a rectangular tank. J. Comput. Phys. 209(1), 47–81 (2005)CrossRefMATH

Chen, J., Beraun, J.: A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems. Comput. Methods Appl. Mech. Eng. 190(1), 225–239 (2000)CrossRefMATH

Chen, Z., Hu, W., Shen, L.M., Xin, X., Brannon, R.: An evaluation of the MPM for simulating dynamic failure with damage diffusion. Eng. Fract. Mech. 69, 1873–1890 (2002)CrossRef

Chen, Z., Zong, Z., Li, H., Li, J.: An investigation into the pressure on solid walls in 2D sloshing using SPH method. Ocean Eng. 59, 129–141 (2013)CrossRef

Chen, Z., Zong, Z., Liu, M.B., Li, H.T.: A comparative study of truly incompressible and weakly compressible SPH methods for free surface incompressible flows. Int. J. Numer. Methods Fluids 73(9), 813–829 (2013)MathSciNet

Chen, Z.P., Qiu, X.M., Zhang, X., Lian, Y.P.: Improved coupling of finite element method with material point method based on a particle-to-surface contact algorithm. Comput. Methods Appl. Mech. Eng. 293(15), 1–19 (2015)MathSciNetCrossRef

Chorin, A.J.: Numerical solution of the Navier-Stokes equations. Math. Comput. 22(104), 745–762 (1968)MathSciNetCrossRefMATH

Colin, F., Egli, R., Lin, F.Y.: Computing a null divergence velocity field using smoothed particle hydrodynamics. J. Comput. Phys. 217(2), 680–692 (2006)MathSciNetCrossRefMATH

Cummins, S.J., Rudman, M.: An SPH projection method. J. Comput. Phys. 152(2), 584–607 (1999)MathSciNetCrossRefMATH

Faltinsen, O.M.: A numerical nonlinear method of sloshing in tanks with two-dimensional flow. J. Ship Res. 22(3), 193–202 (1978)

Faltinsen, O.M., Rognebakke, O.F., Lukovsky, I.A., Timokha, A.N.: Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. J. Fluid Mech. 407, 201–234 (2000)MathSciNetCrossRefMATH

Faltinsen, O.M., Timokha, A.N.: Sloshing, pp. 125–126 (2009)

Fang, J., Parriaux, A.: A regularized lagrangian finite point method for the simulation of incompressible viscous flows. J. Comput. Phys. 227(20), 8894–8908 (2008)MathSciNetCrossRefMATH

Foster, N., Fedkiw, R.: Practical animation of liquids. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pp. 23–30. ACM (2001)

Gilabert, F.A., Cantavella, V.C., Sanchez, E., Mallol, G.: Modelling fracture process in ceramic materials using the Material Point Method. Eur. Phys. Lett. 96, 24002 (2011)CrossRef

Gong, K., Shao, S., Liu, H., Wang, B., Tan, S.K.: Two-phase sph simulation of fluid-structure interactions. J. Fluids Struct. 65, 155–179 (2016)CrossRef

Goudarzi, M.A., Sabbagh-Yazdi, S.R.: Investigation of nonlinear sloshing effects in seismically excited tanks. Soil Dyn. Earthq. Eng. 43, 355–365 (2012)CrossRef

Gui, Q., Dong, P., Shao, S.: Numerical study of ppe source term errors in the incompressible sph models. Int. J. Numer. Meth. Fluids 77(6), 358–379 (2015)MathSciNetCrossRef

Harlow, F.H., Welch, J.E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids 8, 2182–2189 (1965)MathSciNetCrossRefMATH

Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201–225 (1981)CrossRefMATH

Huang, P., Zhang, X., Ma, S.: Shared memory OpenMP parallelization of explicit mpm and its application to hypervelocity impact. CMES Comput. Model. Eng. Sci. 38, 119–147 (2008)MATH

Huang, P., Zhang, X., Ma, S., Huang, X.: Contact algorithms for the material point method in impact and penetration simulation. Int. J. Numer. Methods Eng. 85(4), 498–517 (2011)CrossRefMATH

Hughes, T.J., Liu, W.K., Zimmermann, T.K.: Lagrangian-eulerian finite element formulation for incompressible viscous flows. Comput. Methods Appl. Mech. Eng. 29(3), 329–349 (1981)MathSciNetCrossRefMATH

Ihmsen, M., Cornelis, J., Solenthaler, B., Horvath, C., Teschner, M.: Implicit incompressible SPH. IEEE Trans. Vis. Comput. Graph. 20(3), 426–435 (2014)CrossRef

Kolaei, A., Rakheja, S., Richard, M.J.: A coupled multimodal and boundary-element method for analysis of anti-slosh effectiveness of partial baffles in a partly-filled container. Comput. Fluids 107, 43–58 (2015)MathSciNetCrossRef

Komatsu, K.: Non-linear sloshing analysis of liquid in tanks with arbitrary geometries. Int. J. Non-linear Mech. 22(3), 193–207 (1987)CrossRefMATH

Koshizuka, S., Oka, Y.: Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl. Sci. Eng. 123(3), 421–434 (1996)CrossRef

Lee, E.S., Moulinec, C., Xu, R., Violeau, D., Laurence, D., Stansby, P.: Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. J. Comput. Phys. 227(18), 8417–8436 (2008)MathSciNetCrossRefMATH

Li, J.G., Hamamoto, Y., Liu, Y., Zhang, X.: Sloshing impact simulation with material point method and its experimental validations. Comput. Fluids 103, 86–99 (2014)MathSciNetCrossRef

Lian, Y.P., Liu, Y., Zhang, X.: Coupling of membrane element with material point method for fluid-membrane interaction problems. Int. J. Mech. Mater. Des. 10(2), 199–211 (2014)CrossRef

Lian, Y.P., Zhang, X., Zhang, F., Cui, X.X.: Tied interface grid material point method for problems with localized extreme deformation. Int. J. Impact Eng. 70, 50–61 (2014)CrossRef

Lian, Y.P., Zhang, X., Zhou, X., Ma, Z.T.: A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading. Comput. Methods Appl. Mech. Eng. 200(17–20), 1659–1670 (2011)CrossRefMATH

Liu, M., Shao, J., Chang, J.: On the treatment of solid boundary in smoothed particle hydrodynamics. Sci. China Technol. Sci. 55(1), 244–254 (2012)CrossRef

Liu, P., Liu, Y., Zhang, X.: Internal-structure-model based simulation research of shielding properties of honeycomb sandwich panel subjected to high-velocity impact. Int. J. Impact Eng. 77, 120–133 (2015)CrossRef

Liu, P., Liu, Y., Zhang, X.: Simulation of hyper-velocity impact on double honeycomb sandwich panel and its staggered improvement with internal-structure model. Int. J. Mech. Mater. Des. 12(2), 241–254 (2016)MathSciNetCrossRef

Ma, S., Zhang, X., Lian, Y.P., Zhou, X.: Simulation of high explosive explosion using adaptive material point method. CMES Comput. Model. Eng. Sci. 39(2), 101–123 (2009)MathSciNetMATH

Ma, S., Zhang, X., Qiu, X.M.: Comparison study of MPM and SPH in modeling hypervelocity impact problems. Int. J. Impact Eng. 36, 272–282 (2009)CrossRef

Ma, Z., Zhang, X., Huang, P.: An object-oriented MPM framework for simulation of large deformation and contact of numerous grains. CMES Comput. Model. Eng. Sci. 55(1), 61–87 (2010)

Mast, C.M., Mackenzie-Helnwein, P., Arduino, P., Miller, G.R., Shin, W.: Mitigating kinematic locking in the material point method. J. Comput. Phys. 231(16), 5351–5373 (2012)MathSciNetCrossRef

Miles, J.W.: Resonantly forced surface waves in a circular cylinder. J. Fluid Mech. 149, 15–31 (1984)MathSciNetCrossRefMATH

Monaghan, J.J.: Simulating free surface flows with SPH. J. Comput. Phys. 110(2), 399–406 (1994)CrossRefMATH

Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136(1), 214–226 (1997)CrossRefMATH

Nairn, J.A.: Numerical implementation of imperfect interfaces. Comput. Mater. Sci. 40, 525–536 (2007)CrossRef

Nakayama, T., Washizu, K.: The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems. Int. J. Numer. Methods Eng. 17(11), 1631–1646 (1981)CrossRefMATH

Okamoto, T., Kawahara, M.: Two-dimensional sloshing analysis by lagrangian finite element method. Int. J. Numer. Methods Fluids 11(5), 453–477 (1990)CrossRefMATH

Onate, E.: A finite point method in computational mechanics. Int. J. Numer. Methods Eng. 39, 3839–3866 (1996)CrossRefMATH

Shao, S., Lo, E.Y.: Incompressible sph method for simulating newtonian and non-newtonian flows with a free surface. Adv. Water Resour. 26(7), 787–800 (2003)CrossRef

Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77(2), 439–471 (1988)MathSciNetCrossRefMATH

Sulsky, D., Chen, Z., Schreyer, H.L.: A particle method for history-dependent materials. Comput. Methods Appl. Mech. Eng. 118(1–2), 179–196 (1994)MathSciNetCrossRefMATH

Tan, H.L., Nairn, J.A.: Hierarchical, adaptive, material point method for dynamic energy release rate calculations. Comput. Methods Appl. Mech. Eng. 191(19–20), 2095–2109 (2002)MATH

Tang, B., Li, J., Wang, T.: The least square particle finite element method for simulating large amplitude sloshing flows. Acta Mech. Sin. 24(3), 317–323 (2008)CrossRefMATH

Tran, L.T., Kim, J., Berzins, M.: Solving time-dependent PDEs using the material point method, a case study from gas dynamics. Int. J. Numer. Methods Fluids 62(7), 709–732 (2010)MathSciNetMATH

Wu, C.H., Faltinsen, O.M., Chen, B.F.: Numerical study of sloshing liquid in tanks with baffles by time-independent finite difference and fictitious cell method. Comput. Fluids 63, 9–26 (2012)MathSciNetCrossRefMATH

Yang, X., Liu, M., Peng, S.: Smoothed particle hydrodynamics modeling of viscous liquid drop without tensile instability. Comput. Fluids 92, 199–208 (2014)MathSciNetCrossRef

York, A.R., Sulsky, D., Schreyer, H.L.: Fluid-membrane interaction based on the material point method. Int. J. Numer. Methods Eng. 48, 901–924 (2000)CrossRefMATH

Zhang, F., Zhang, X., Sze, K.Y., Lian, Y., Liu, Y.: Incompressible material point method for free surface flow. J. Comput. Phys. 330, 92–110 (2017)MathSciNetCrossRefMATH

Zhang, X., Chen, Z., Liu, Y.: The Material Point Method - A Continuum-Based Particle Method for Extreme Loading Cases. Academic Press, London (2016)

Zhu, Y.N., Bridson, R.: Animating sand as a fluid. ACM Trans. Graph. (TOG) 24(3), 965–972 (2005)CrossRef

Title: An augmented incompressible material point method for modeling liquid sloshing problems
Authors: Fan Zhang
Xiong Zhang
Yan Liu
Publication date: 20-02-2017
Publisher: Springer Netherlands
Published in: International Journal of Mechanics and Materials in Design / Issue 1/2018
Print ISSN: 1569-1713
Electronic ISSN: 1573-8841
DOI: https://doi.org/10.1007/s10999-017-9366-5

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