Higher-order functions give smoother distributions, but generally require a larger computational load. Since the spatial derivative corresponds to the derivative of the kernel in the SPH method, as described below, a third-order B-spline kernel that is linear with respect to the second-order derivative is the lowest order kernel that is acceptable.

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Principles of Conventional Particle Methods

  • Hitoshi Gotoh,
  • Abbas Khayyer

摘要

Higher-order functions give smoother distributions, but generally require a larger computational load. Since the spatial derivative corresponds to the derivative of the kernel in the SPH method, as described below, a third-order B-spline kernel that is linear with respect to the second-order derivative is the lowest order kernel that is acceptable.