Comparative Study and Improvements on Mesh-free Lagrangian Computational Fluid Dynamics
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Mesh-free Lagrangian Computational Fluid Dynamics is a numerical scheme where the computational points are represented by freely-moving finite particles that have a constant mass. Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi Implicit (MPS) method are two prominent methods that utilized the above-mentioned framework. Both methods principal advantages are best exploited when simulating large deformation and fragmentation of free surface. Although sharing the same framework, both methods have several differences, especially in the formulation of density-pressure coupling. The classical test cases of particle method, a two-dimensional broken dam and forced harmonic oscillated sloshing tank, are selected for a comparative study. The broken dam problem is used for quantitatively compare the SPH and the MPS viscous parameters. The broken dam problem is also used to compare the free surface snapshots of both methods and the corresponding experiment results. In the harmonic oscillated sloshing tank problem, impact pressure at the wall of the tank is investigated. The pressure profile from SPH and MPS method is then qualitatively compared against the corresponding experiments. The strong and weak points of the two particle methods are extensively discussed. Through the comparative study, several minor differences were observed. MPS is typically computationally more intensive in dealing with large number of particles due to the pressure Poisson equation. In contrast, SPH is computationally more efficient than MPS; however, pressure fluctuation can be problematic in dynamic analysis. Another problem is observed on the boundary treatment. In the SPH, unphysical gap between fluid particles and wall particles is observed. The unphysical gap is then removed using the newly implemented boundary condition that utilized force balance relation between the wall and fluid particles. No particle penetration is further ensured by introducing the collision model. Because of the absence of shear viscous term in the newly implemented boundary condition formulation, the method perform poorly when violent boundary movement in transversal direction is involved. A dam break case, a sloshing tank case, and a piston wave maker case with physical absorbing layer is modeled using the improved boundary condition. The physical absorbing layer successfully absorbed the incoming wave energy without the need of further mathematical manipulation.
Bakti, Farid Putra (2015). Comparative Study and Improvements on Mesh-free Lagrangian Computational Fluid Dynamics. Master's thesis, Texas A & M University. Available electronically from