Direct imposition of the wall boundary condition for weakly compressible flows in three-dimensional smoothed particle hydrodynamics simulations

Abstract

This study introduces a novel method for imposing wall boundary conditions in smoothed particle hydrodynamics (SPH). SPH is a particle method based on the Lagrangian approach, primarily employed in fluid analysis as a part of numerical computation methods. Due to its ability to discretize space using particles, SPH excels in handling analyses of free surface flow or multiphase flow with intricate boundary surfaces. However, there is a drawback in modeling wall boundaries using particles, as resolving the particle deficiency problem necessitates multi-layered boundary particles to be arranged behind the wall boundary. This leads to difficulties in implementing complex shapes and adds computational expense. To address this issue, this study suggests the use of boundary segments for wall boundary modeling and specifically employs triangular segments for three-dimensional expansions. For robust application of boundary conditions, a method considering both Poisson's equation and geometric configurations is proposed. The proposed method is independent of the segment density, which facilitates efficient and flexible modeling. In addition, by imposing accurate boundary conditions from the wall, the stability and accuracy of the solution are enhanced. The performance of the proposed method is validated through numerical examples, compared with various analytical and experimental results.