Abstract

Internal erosion, caused by seepage flow inside the soil, accelerates soil failure during a natural disaster. Numerical simulation can be an effective tool to quantitatively evaluate the relationship between internal erosion and the instability of the ground as a whole. Internal erosion and multiphase flow simulation of fluid and granular materials with a particle size distribution require coupling simulations that can represent the interaction between particles and pore water and the movement of particles. There are two main types of coupling models: ”Resolved coupling model,” which can calculate detailed flow and fluid forces, and ”Unresolved coupling model,” which is based on empirical drag and seepage flow models. Previous studies have indicated that both models should be judged appropriately based on the ratio of particle-fluid spatial resolution. However, applying a resolved coupling model to the vast number of soil particles that make up the ground is impractical from a computational cost perspective, and empirical unresolved coupling model has difficulty in representing localized failures such as internal erosion. Therefore, developing a new coupling model that satisfies both computational accuracy and efficiency is desirable. In this study, we applied ISPH (Incompressible Smoothed Particle Hydrodynamics) for fluid analysis and DEM (Discrete Element Method) for soil particles to develop a fluid-soil coupling simulation model that can directly represent the movement of soil particles during the internal erosion process. Through numerical experiments using a particle layer with the vertical upward flow, we understand the limitations of the conventional coupling model and propose a new hybrid type of semi-resolved coupling model that combines these two models appropriately.

Abstract

Incompressible fluid analysis using the ISPH or MPS methods requires the solution of the pressure Poisson equation, which takes up most of the overall computation time. In addition, the iteration number for solving pressure Poisson equations may increase as the simulation model scale increases. This is a common problem in particle methods and the other implicit time integration solvers. In different methods, FEM, etc., good quality preconditioning, such as multigrid preconditioning, can significantly improve the convergence of iterative solution methods. There are two types of multigrid preconditioners, algebraic multigrid and geometric multigrid methods, but there are few examples of their application in particle methods. In this study, we attempted to develop a framework for a geometric multigrid preconditioner for solving the pressure Poisson equation in the ISPH. First, we focused on the geometric multigrid preconditioner using background cells, which are used for neighboring particle search, and implemented it on a GPU environment. Through a simple dam-break problem, we compared the computation time between the Conjugate gradient (CG) solver with a traditional preconditioner and the CG solver with a geometric multigrid preconditioner. We confirmed that the background cell-based geometric multigrid preconditioner is practical for the ISPH method.

Abstract

Particle methods such as the SPH and MPS methods have problems because it is difficult to treat curved bottom surfaces such as seabed surfaces accurately. In this study, regarding this problem, the curved bottom surfaces’ treatments have been improved using a coordinate transformation using the high-order second derivative model called SPH(2). Although the theory for the coordinate transformation was established in the MPS method, its accuracy did not give the desired accuracy because of the numerical errors of the second derivative models. Therefore, the numerical errors in these coordinate transformations were overcome by applying the second derivative model of SPH(2) to the coordinate transformation formulas. The superiority and validity of the proposed coordinate transformation using SPH(2) are demonstrated through validation examples such as the hydrostatic pressure and dam-break problems.