title: An improved impermeable solid boundary scheme for the MLPG_R method and a two-phase ISPH model for suspended sediment-laden flows
Creators: name: Pan, Xinglin
Publisher: name: University of Liverpool Repository
Year: 2022

description: Over the past decades, meshless methods have become an essential numerical tool for simulating a wide range of science and engineering problems. The key idea of the meshless methods is to provide accurate and stable numerical solutions, where the computation domain is discretized using particles instead of using conventional meshes. In this thesis, developments on the Meshless Local Petrov-Galerkin (MLPG) method and incompressible smoothed particle hydrodynamics (ISPH) have been carried out for rigid boundary condition implementation and simulation of dispersed two-phase flows, respectively. For rigid boundary condition implementation in the MLPG method, an improved boundary scheme is developed through a weak formulation for the boundary particles based on Pressure Poisson Equation (PPE). In this scheme, the wall boundary particles simultaneously satisfy the PPE in the local integration domain by adopting the MLPG method with the Rankine source solution (MLPG_R) integration scheme (Ma, 2005b) and the pressure Neumann boundary condition. The new weak formulation vanishes the derivatives of the unknown pressure at wall particles and is discretized in the truncated support domain without extra artificial treatment. This improved boundary scheme is validated by analytical solutions, numerical benchmarks, and experimental data in the cases of patch tests, lid-driven cavity, flow over a cylinder and monochromic wave generation. The numerical results show higher accuracy in pressure and velocity, especially near the boundary, compared to the existing boundary treatment methods that directly discretize the pressure Neumann boundary condition. For two-phase meshless model development, the incompressible SPH method is developed for simulating suspended sediment transport problems. The fluid and sediment are treated as two continuous phases described by two sets of Navier-Stokes equations with interactions between two phases achieved by the drag force. The computational domain is discretized into a single set of SPH particles which move with the fluid velocity but carry the local properties of both phases, including sediment velocity and its volume fraction. In addition, large eddy simulation (LES) is employed for representing the turbulent effect, in which the eddy viscosities are defined by the Smagorinsky model. The pressure Neumann boundary condition is imposed on the rigid solid walls and the zero pressure boundary condition on the free water surface. The two-phase model is verified by the analytical solutions for two idealized problems of still water with neutrally buoyant sediment and still water with naturally settling sediment in a two-dimensional water tank. The model is then applied to the study of sand dumping. It is shown that the characteristics of the settling sand cloud, the pressure field, and the flow vortices are in good agreement with experimental results. The proposed two-phase model is proven to be effective for the numerical study of suspended sediment problems.