Accuracy and Stability of Smoothed Particle Hydrodynamics in Fluid-Structure Interaction Problems

An inevitable consequence of advances in computational power is humankind’s growing curiosity towards better understanding of its surroundings. Various methods and algorithms have been developed to address this curiosity by numerical modeling of complex problems. Smoothed particle hydrodynamics (SPH) is a numerical method that relies on approximating physical quantities through interactions of discrete points possessing individual material properties. Initially applied to study rotating polytropes, the usage areas have since then been extended to modeling of elasticity, fracture, heat transfer and incompressible flows. However, despite its relatively long history, the applicability of SPH for viscous incompressible internal flows is not fully understood and its limitations have not been fully assessed. This thesis is devoted to study the behavior of SPH when applied to such flows. Majority of the previous studies have studied the ability of SPH to capture flow phenomenon focusing primarily on mean integral quantities. This thesis underlines that ability of a method to model a phenomenon on a mean scale does not necessarily prove its viability to study problems where instantaneous flow structures play a role. Being an explicit numerical method, an instability in an instantaneous solution field might get amplified without being noticed, and adversely affects long term behavior. The accuracy and performance are tested through cases operating at a wide range of Reynolds numbers involving stationary as well as freely moving objects. The ability of SPH to model transitional flows past a stationary object, the effect of different viscous diffusion formulations on the solution field as well as its stability characteristics are analyzed. Relationship between the numerical speed of sound and the density field, along with the continuity equation formulations are also extensively investigated in a two-dimensional configuration with a freely migrating object using standard SPH and its commonly used variant. To improve its stability in such problems, a correction to the parameter controlling density diffusion is proposed. The understanding following these tests is then applied to model inertial migration of a neutrally buoyant sphere in a pipe with periodic corrugations both to test SPH in three-dimensional problems and to explain the physical mechanism responsible in such a migration.