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K2_SPH method and its application for 2-D water wave simulation

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Abstract

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian meshless particle method. However, its low accuracy of kernel approximation when particles are distributed disorderly or located near the boundary is an obstacle standing in the way of its wide application. Adopting the Taylor series expansion method and solving the integral equation matrix, the second order kernel approximation method can be obtained, namely K2_SPH, which is discussed in this paper. This method is similar to the Finite Particle Method. With the improvement of kernel approximation, some numerical techniques should be adopted for different types of boundaries, such as a free surface boundary and solid boundary, which are two key numerical techniques of K2_SPH for water wave simulation. This paper gives some numerical results of two dimensional water wave simulations involving standing wave and sloshing tank problems by using K2_SPH. From the comparison of simulation results, the K2_SPH method is more reliable than standard SPH.

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Authors and Affiliations

  1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, China

    Zhenhong Hu, Xing Zheng & Wenyang Duan

  2. School of Engineering and Mathematical Science, City University, London, EC1V 0HB, UK

    Qingwei Ma

Authors
  1. Zhenhong Hu
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  2. Xing Zheng
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  3. Wenyang Duan
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  4. Qingwei Ma
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Corresponding author

Correspondence to Xing Zheng.

Additional information

Foundation item: Supported by the National Natural Science Fundation of China (51009034), Foundational Research Funds of Harbin Engineering University (HEUFT05023, HEUFP05001), Foundational Research Funds for the central Universities (HEUCF100102) and 111 program (B07019).

Zhenhong Hu was born in 1976. She is a lecturer at Harbin Engineering University. Her current research interests include hydrodynamics and the meshless computation method.

Xing Zheng was born in 1980. He is a lecturer at Harbin Engineering University. His current research interests include the meshless computation method and hydrodynamics.

Wenyang Duan was born in 1967. He is a professor at Harbin Engineering University. His current research interests include marine hydrodynamics, time domain BEM, and meshless particle methods.

Qingwei Ma was born in 1955. He is a professor at the City University of London. His current research interests include meshless particle method algorithms and the nonlinear finite element method for hydrodynamics simulation.

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Hu, Z., Zheng, X., Duan, W. et al. K2_SPH method and its application for 2-D water wave simulation. J. Marine. Sci. Appl. 10, 399–412 (2011). https://doi.org/10.1007/s11804-011-1085-y

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  • DOI: https://doi.org/10.1007/s11804-011-1085-y

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