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<p>Smoothed Particle Hydrodynamics (SPH), a widely-used numerical method for simulating fluid flows with complex interfaces and boundaries, has undergone decades of development. This paper reviews the efforts towards advancing high-order SPH and its applications. The fundamentals of SPH are briefly introduced, followed by an analysis of errors arising in kernel and particle approximations. The relationship between consistency and accuracy is also discussed. To achieve high-order accuracy, this paper details three approaches: correcting SPH derivative operators, constructing kernel functions and implementing spatial reconstructions in the Riemann-SPH formulation. Finally, the applications of these high-accuracy SPH methods are described to show their potential for further development.</p>

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High-order SPH: A Review of the Method and Applications

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Zi-Fei Meng,
  • Peng-Nan Sun,
  • Ping-Ping Wang,
  • Boo Cheong Khoo,
  • A.-Man Zhang

摘要

Smoothed Particle Hydrodynamics (SPH), a widely-used numerical method for simulating fluid flows with complex interfaces and boundaries, has undergone decades of development. This paper reviews the efforts towards advancing high-order SPH and its applications. The fundamentals of SPH are briefly introduced, followed by an analysis of errors arising in kernel and particle approximations. The relationship between consistency and accuracy is also discussed. To achieve high-order accuracy, this paper details three approaches: correcting SPH derivative operators, constructing kernel functions and implementing spatial reconstructions in the Riemann-SPH formulation. Finally, the applications of these high-accuracy SPH methods are described to show their potential for further development.