Application of the Godunov-Type Corrective Smoothed Particle Method to Impulsive Load Studies

Document Type : Regular Article


1 Key Laboratory of Microgravity (National Microgravity Laboratory), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, P.R. China

2 School of Architectural Engineering, Kunming University of Science and Technology, Kunming 650500, P.R. China



The smoothed particle hydrodynamics (SPH) method is based on the kernel particle approximation, which is sensitive to the uniformity of the SPH particle distribution in the computational domain; that is, all SPH particles must be distributed evenly in the computational domain. These factors significantly influence the practical application of the SPH method. Meanwhile, calculating the sum near the boundaries of the computational domain may cause boundary defect problems since there are insufficient particles in the support domain, thus often resulting in relatively high errors in numerical simulation results near boundaries. To address these problems, the kernel particle approximation discrete process was corrected based on the traditional SPH method, and the corrected SPH method, the Godunov-type corrective smoothed particle method (CSPM), was formulated by introducing Riemann decomposition. In this study, the traditional SPH method and Godunov-type CSPM method were applied in a comparative study of discontinuous function problems, 1D shock tubes and 1D detonation waves. According to the analysis results, the Godunov-type CSPM method can not only effectively improve the calculation accuracy and compatibility of the traditional SPH method in discontinuous shock wave problems but also increase the accuracy of the traditional SPH method in capturing strong discontinuities.


Abdelrazek, A. M., I. Kimura and Y. Shimizu (2014). Comparison between SPH and MPS methods for numerical simulations of free surface flow problems. Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering) 70(4), I_67–I_72.##
Bakti, F. P., M. H. Kim, K. S. Kim and J. C. Park (2016). Comparative study of standard WC-SPH and MPS solvers for free surface academic problems. International Journal of Offshore and Polar Engineering 26(3), 235–243.##
Chen, J. K. and J. E. Beraun (2000). A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineering 190(1/2), 225–239.##
Chen, X. and D. C. Wan (2019). Numerical simulation of liquid sloshing in LNG tank using GPU-accelerated MPS method. Chinese Journal of Theoretical and Applied Mechanics 51(3), 714–729.##
Chen, X., Y. L. Zhang and D. C. Wan (2018). Developments of the MPS method and its applications on hydrodynamics problems. Journal of Harbin Engineering University 39(6), 955–972.##
Chen, Y. D., F. Lu, H. S. Sun, C. Z. Gong, M. B. Cao, and J. D. Cai (2020). Study on bearing behavior of uplift pile based on discrete element method. Water Resources and Hydropower Engineering 51(9), 200–204.##
Gao, W. R., H. F. Qiang and S. Y. Zhang (2007). Godunov-type corrective smoothed particle method (CSPM). Chinese Journal of Computational Mechanics 24(5), 638–642.##
Gingold, R. A. and J. J. Monaghan (1977). Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society 181(3), 375–389.##
Gu, S. L., Y. S. Wu, H. W. Xie and X. W. Yuan (2016). CSPM method-based numerical simulation on outflow from 2-D pipe nozzle. Water Resources and Hydropower Engineering 47(9), 39–43.##
Hashimoto, H., N. Grenier, M. Sueyoshi and D. L. Touze (2022). Comparison of MPS and SPH methods for solving forced motion ship flooding problems. Applied Ocean Research 118, 103001.##
Inutsuka, S. (1994). Godunov-type SPH. Memorie Della Societa Astronomica ltaliana 65(4), 1027–1031.##
Kloss, C., C. Goniva, A. Hager, S. Amberger and S. Pirker (2012). Models, algorithms and validation for opensource DEM and CFD-DEM. Progress in Computational Fluid Dynamics an International Journal 12(2/3), 140–152.##
Liu, G. R. and M. B. Liu (2003). Smoothed Particle Hydrodynamics: A Meshfree Particle Method. Singapore: World Scientific Publishing Co. Pte. Ltd.##
Liu, M. B. and S. M. Li (2016). On the modeling of viscous incompressible flows with smoothed particle hydro-dynamics. Journal of Hydrodynamics, Ser. B 28(5), 731–745.##
Liu, M. B., G. R. Liu and K. Y. Lam (2003a). A one-dimensional meshfree particle formulation for simulating shock waves. Shock Waves 13(3), 213–220.##
Liu, M. B., G. R. Liu, K. Y. Lam and Z. Zong (2003b). Smoothed particle hydrodynamics for numerical simulation of underwater explosion. Computational Mechanics 30(2), 106–118.##
Lucy, L. B. (1977). A numerical approach to the testing of the fission hypothesis. The Astronomical Journal 82(12), 1013–1024.##
Ma, L. Q., M. B. Liu, J. Z. Chang, T. X. Su and H. T. Liu (2012). Numerical simulation of droplet impact onto liquid films with smoothed particle hydrodynamics. Acta Physica Sinica 61(24), 244701.##
Monaghan, J. J. (1982). Why particle methods work. SIAM Journal on Scientific & Statistical Computing 3(4), 422–433.##
Monaghan, J. J. (1997). SPH and Riemann solvers. Journal of Computational Physics 136(2), 298–307.##
Morris, J. P. and J. J. Monaghan (1997). A switch to reduce SPH viscosity. Journal of Computational Physics 136(1), 41–50.##
Parshikov, A. N. and S. A. Medin (2002). Smoothed particle hydrodynamics using interparticle contact algorithms. Journal of Computational Physics 180(1), 358–382.##
Robb, D. M., S. J. Gaskin and J. C. Marongiu (2016). SPH-DEM model for free-surface flows containing solids applied to river ice jams. Journal of Hydraulic Research 54(1), 27–40.##
Sun, P. N. (2018). Study on SPH Method for the Simulation of Object-Free Surface Interactions. Ph. D. thesis, Harbin Engineering University, Harbin, China.##
Sun, X. S., M. Sakai and Y. Yamada (2013). Three-dimensional simulation of a solid-liquid flow by the DEM-SPH method. Journal of Computational Physics 248, 147–176.##
Tian, X. and D. C. Wan (2019). Simulation of sloshing in three-dimensional cylindrical tank by MPS method. Chinese Journal of Ship Research 14(3), 116–121.##
Wang, X. J., G. M. Zhang, W. T. Liu and Z. Zhou (2002). Computations of elastic-plastic waves by smoothed particle hydrodynamics. Explosion and Shock Waves 22(2), 97–103.##
Xu, Y., Q. C. Sun, L. Zhang and W. B. Huang (2003). Advances in discrete element methods for particulate materials. Advances in Mechanics 33(2), 251–260.##
Zhang, S. C. (1996). Smoothed particle hydrodynamics (SPH) method (A Review). Chinese Journal of Computational Physics 13(4), 385–397.##
Zheng, W. G., Y. Wang, Y. Y. Zhang, L. Q. Ren and S. L. Gu (2020). SPH method-based study on energy dissipation characteristics of stepped spillway. Water Resources and Hydropower Engineering 51(12), 117–124.
Volume 15, Issue 6 - Serial Number 67
November and December 2022
Pages 1889-1899
  • Received: 18 March 2022
  • Revised: 20 July 2022
  • Accepted: 01 August 2022
  • First Publish Date: 07 September 2022