High order smoothed particle hydrodynamic methods for slightly compressible bounded flow

He, Zhenyu
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University of Delaware
This thesis investigates the accuracy and the implementation of solid wall boundary conditions for Smoothed Particle Hydrodynamics (SPH) for the simulation of slightly compressible fluid flows. The accuracy of SPH is affected by two key parameters: the smoothing length and the overlap. Investigation of the convergence of SPH is conducted on a two-dimensional doubly periodic flow. The result shows that the standard SPH formulation does not converge with a fixed rate and the overall error is limited by the discretization error with a fixed overlap value. New algorithms are developed for the approximations of gradient operator and laplacian operator that have third order convergence rate with a fixed overlap value. In order to generate the model efficiently and maintain accuracy an appropriate boundary treatment is important. Two existing boundary treatments are investigated: the ghost particle method and the boundary force method. Those methods have their advantage and disadvantage. The ghost particle method works well for boundaries with straight lines or flat plane but it is difficult to implement for boundaries with complex geometry. The boundary force method is easy to handle boundaries with complex geometry but one of the parameters is application dependent. A new boundary technique is developed based on the new SPH approximation algorithms. The new boundary treatment adopts the ability to handle curved boundaries from the boundary force method without any free parameters. The algorithms were tested through SPH simulations of doubly periodic flow, plane Couette Flow and circular Couette flow. The determined velocity profiles agree well with theoretical results. The results of the convergence study show that the new algorithms are high-order methods and better than currently existing techniques.