Bottom Boundary-Fitted Free Surface Flow Simulation with Coordinate Transformation Using SPH(2)

  • Fujioka, Shujiro (Kyushu Universiy)
  • Tsuji, Kumpei (Tohoku University)
  • Mitsume, Naoto (Tsukuba University)
  • Asai, Mitsuteru (Kyushu University)

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The original SPH performs interpolation and numerical differentiation with a fixed kernel function depending on the distance from the particle of interest to its neighbors, thus guaranteeing accuracy only if the particles are regularly and uniformly distributed. SPH uses the well-known modified gradient operator to improve accuracy up to the first order in terms of particle distance. On the other hand, second-order differential (Laplacian) and higher-order gradient models are less discussed. We, therefore, have proposed a second-order SPH model, SPH(2), that satisfies second-order accuracy in both first- and second-order derivatives. The key idea is based on the LDD particle method proposed by Basic et al. The results confirmed the superiority of SPH(2) over the existing SPH models. In this study, we take advantage of second-order accuracy in the first and second-derivative operators including cross-derivative, and perform coordinate transformations using SPH(2). In order to make effective use of SPH(2) in coastal engineering, it is necessary to reduce the heavy computational cost of the particle method by performing coordinate transformations such as the σ-coordinate system. Therefore, as the first step of the σ-coordinate system SPH, we implemented the bottom boundary fitting coordinate transformation in SPH(2) so that complex outer solid boundary shapes seen in the physical domain can be treated as simple straight boundaries in the computational domain. Comparison with experimental results shows that SPH(2) is effective and superior to conventional methods in the analysis using the coordinate transformation.