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Dynamic refinement and boundary contact forces in smoothed particle hydrodynamics with applications in fluid flow problems. / Jonathan Feldman

Swansea University Author: Jonathan Feldman

Abstract

Smoothed Particle Hydrodynamics (SPH) is a relatively new, simple and effective numerical method that can be used to solve a variety of difficult problems in computational mechanics. It is a fully Lagrangian meshless method ideal for solving large deformation problems such as complex free surface fl...

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Published: 2006
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42459
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Abstract: Smoothed Particle Hydrodynamics (SPH) is a relatively new, simple and effective numerical method that can be used to solve a variety of difficult problems in computational mechanics. It is a fully Lagrangian meshless method ideal for solving large deformation problems such as complex free surface fluid flows. This research was carried out with the support of BAE Systems and falls into two distinct areas. Firstly to investigate new methods for treating fixed boundaries and secondly to investigate refinement algorithms which allow for both sparsely and densely populated regions of particles within the same computational domain. Much work has been done in the modelling of particle-boundary interactions in SPH since the governing equations do not naturally incorporate essential boundary conditions. In this research a new technique for calculating boundary contact forces is developed. The forces are obtained from a variational principle and as such conserve both the linear and angular momentum of the system. The boundaries are explicitly defined using this new approach and so the need for additional boundary particles is removed. In the past most SPH derivations have been based on a uniform distribution of particles of equal mass. This leads to large simulations with many particles and long run times. In other mesh based schemes it has become common place to use mesh adaptivity to improve numerical results and reduce computation times. With a corresponding refinement strategy SPH can gain these same advantages. In this research a refinement strategy based upon particle splitting is developed. Candidate particles are split into several 'daughter' particles according to a given refinement pattern centred about the original particle position. Through the solution of a non-linear minimisation problem the optimal mass distribution for the daughter particles is obtained so as to reduce the errors introduced into the underlying density field. This procedure necessarily conserves the mass of the system. The unique daughter particle velocity configuration that conserves the linear and angular momentum of the system is also identified. The conclusion of the research was the successful implementation of these improvements into the existing SPH framework. As a result the capability and flexibility of the code is greatly increased and the computational expense needed for running large simulations has been reduced.
Keywords: Computational physics.;Fluid mechanics.
College: Faculty of Science and Engineering

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