
Improvement of Wall Boundary Treatment using Velocity-Pressure Monolithic SPH Fluid Analysis Algorithm
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Smoothed Particle Hydrodynamics (SPH) method demonstrates high applicability for free surface flows and large deformation problems. However, Incompressible SPH (ISPH) method, an application of SPH for incompressible fluids, faces a significant drawback: it cannot accurately compute solutions when multiple wall boundaries exist in the vicinity of fluid particles. This is due to the fact that fluid particles are imposed multiple different Neumann boundary conditions. To overcome this drawback, we propose a novel ISPH method (Monolithic ISPH) capable of handling arbitrary wall boundary geometries. A key feature of this method is that it eliminates the need for Neumann boundary conditions at wall boundaries, requiring only Dirichlet boundary conditions for boundary treatment. This enables the application to problems with arbitrary wall boundaries that were difficult to implement using conventional ISPH methods. Furthermore, following the approaches in FEM and MPM literature [1], this method incorporates stabilization using Variational Multiscale (VMS) method [2], which allows stable formulation of the coupled velocity-pressure equation. The effectiveness of the proposed method was verified through various numerical examples, including hydrostatic pressure problems with constrictions and dynamic dam break problems. Another notable feature of this method is the elimination of the conventional three-layer wall particle requirement, enabling boundary treatment with just a single layer of wall particles. This advancement not only overcomes the drawback of conventional approaches but also achieves implementation simplicity. As future prospects, we plan to expand to three-dimensional problems. To address the associated increase in computational cost, we intend to implement GPU parallel computing and multigrid preconditioner solvers. Ultimately, we aim to apply this method to practical engineering problems such as analysis of pore water flow in soil.