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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 101
Edited by:
Paper 42

Parallel Algorithms for Smoothed Particle Hydrodynamics and Dissipative Particle Dynamics

M. Ivanovic1, N. Filipovic2, B. Stojanovic1 and M. Kojic3

1Faculty of Science, University of Kragujevac, Serbia
2Faculty of Engineering, University of Kragujevac, Serbia
3The Methodist Hospital Research Institute, Houston TX, United States of America

Full Bibliographic Reference for this paper
M. Ivanovic, N. Filipovic, B. Stojanovic, M. Kojic, "Parallel Algorithms for Smoothed Particle Hydrodynamics and Dissipative Particle Dynamics", in , (Editors), "Proceedings of the Third International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 42, 2013. doi:10.4203/ccp.101.42
Keywords: computational fluid dynamics, microfluids, parallel processing, particle methods.

Conventional numerical methods for solving PDEs are a priori based on the existence of a permanent connection among nodes of the mesh. In cases of solving fluid flow problems with large changes in the model of the domain and problems including fluids with free surfaces, the mesh deforms considerably, which may lead to large errors in solutions. Relatively new class of methods, the "mesh-free methods'', resolves the connection among nodes at the run time. Smoothed particle hydrodynamics (SPH) is one of the most relevant and most convenient of the the mesh-free methods.

By contrast with classical macroscopic methods, either mesh based or mesh free, show certain deficiencies in the modelling of complex fluids, such as colloidal mixtures characteristic for biological systems. These kinds of fluids, although having a homogeneous macroscopic appearance, are highly heterogeneous due to thermal fluctuations and complex reactions among their constituents. One of the numerical approaches suitable for modelling such phenomena are meso-scale methods, designed in a way to conform to both microscopic and macroscopic laws of fluid flow. Historically speaking, such meso-scale methods are a step in the direction of overcoming problems of large numbers of degrees of freedom and very low critical time steps in strict the molecular dynamics (MD) method. With meso-scale methods such as dissipative particle dynamics (DPD), molecular phenomenology can be modelled to a certain degree using today's computers, which was completely unfeasible with the MD method.

In this paper an implementation, is presented, of a reusable, cross-platform, object-oriented parallel framework written in C++, suitable for modelling all kinds of mesh free or/and particle phenomena, including methods such as SPH, DPD and MD. The code handles one-, two- and three-dimensional problems, using a domain decomposition technique and a standard distributed memory approach along with the MPI standard. The particle (integration point) search algorithm employs the nearest neighbour algorithm with possibly a variable radius (dilatation parameter in SPH). The algorithms capable of handling all kinds of boundary conditions, including bounce-back, periodic, prescribed values are incorporated into the code.

Various performance benchmarks have been performed, primarily using the SPH approach, the major focus of the proposed framework. The first performance test is a guideline of how to prepare a model for a parallel run in order to achieve better speed-up, regarding primarily the size of the inter-process interfaces. The second benchmark demonstrates the influence of the MPI message length on speed-up and parallel efficiency, along with the study of how to employ multiprocessor computing nodes in order to achieve lower run times with modern hardware resources. The lastbenchmark demonstrates how the domain decomposition deals with various showcases with largely different natures, but is yet realistic. These showcases vary from one to three-dimensional models, some with regular and others with a largely deforming computational domain, posing various issues to incorporate the neighbour search and domain decomposition algorithms.

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