Topography-based and vectorized algorithm for extracting physical quantities in 3D-SPH form and its application in debris-flow entrainment modeling

Extraction of physical quantities such as flow depth and velocities, is one of the major purposes of geophysical flow numerical modeling and critical for estimating consequent impact forces and sediment entrainment. It is simple in nature for mesh-based models but presenting challenges in three-dimensional smoothed particle hydrodynamics (SPH) schemes. The difficulties lie in the substantial number of particles and their uneven spatial-temporal distribution, particularly over complex topography. Inspired by our previous surface cell (SC) -based approach, we propose a novel topography-based and vectorized algorithm that significantly enhances the ability to extract physical quantities over complex topography. In the proposed algorithm, geomorphologic characteristics are mathematically represented by topographical normal vectors. The correlations of physical quantities with distinct coordinate descriptions are established through the vectorization concept, ultimately leading to effective extraction of physical quantities in SPH form over complex topography. This algorithm provides an important tool to incorporate topography-linked physical models within discretized frameworks. To validate its effectiveness, we employed the algorithm to integrate the debris-flow entrainment law with our previous HBP-SPH model, utilizing the 2010 Yohutagawa debris-flow event in Japan as a case study. The results demonstrate a good agreement between the numerical simulation and on-site observation. Discussion regarding the applicability and limitation of the algorithm concludes the paper.