MPS-Based Shallow Water Simulation with Particle Splitting for Tsunami Runnup

  • Saigo, Iori (The University of Tokyo)
  • Koshizuka, Seiichi (The University of Tokyo)

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This study proposes a numerical method for solving the 2D shallow water equations (SWEs) to predict tsunami runup correctly and efficiently. The method is based on the moving particle semi-implicit (MPS) method, a type of particle method. A newly developed dynamic particle splitting method was introduced to maintain spatial resolution in low-water regions. When considering tsunami-like phenomena where the depth scale is sufficiently small compared to the horizontal scale, the distribution of physical quantities in the depth direction is unimportant. Based on this idea, SWEs are derived from the depth-integration of the equation of motion and Navier-Stokes equations. Solving the SWEs instead of the Navier-Stokes equations reduces the number of dimensions in the computational space, thus saving computational time. A challenge in solving SWEs with particle methods is the reduction of spatial resolution in regions of low water levels. This is particularly problematic for analyses such as tsunami runup, where detailed results should be obtained primarily in areas of low water depth. To address this issue, we have developed and implemented a dynamic particle splitting method in this paper. Benchmark tests were conducted using the proposed method, and the results were in good agreement with both the analytical solutions and experimental results.