An investigation of a finite volume method incorporating radial basis functions for simulating nonlinear transport

Moroney, Timothy John (2006) An investigation of a finite volume method incorporating radial basis functions for simulating nonlinear transport. PhD thesis, Queensland University of Technology.


The objective of this PhD research programme is to investigate the effectiveness of a finite volume method incorporating radial basis functions for simulating nonlinear transport processes. The finite volume method is the favoured numerical technique for solving the advection-diffusion equations that arise in transport simulation. The method transforms the original problem into a system of nonlinear, algebraic equations through the process of discretisation. The accuracy of this discretisation determines to a large extent the accuracy of the final solution.

A new method of discretisation is presented that employs radial basis functions (rbfs) as a means of local interpolation. When combined with Gaussian quadrature integration methods, the resulting finite volume discretisation leads to accurate numerical solutions without the need for very fine meshes, and the additional overheads they entail.

The resulting nonlinear, algebraic system is solved efficiently using a Jacobian-free Newton-Krylov method. By employing the new method as an

extension of existing shape function-based approaches, the number of nonlinear iterations required to obtain convergence can be reduced. Furthermore, information obtained from these iterations can be used to increase the efficiency

of subsequent rbf-based iterations, as well as to construct an effective parallel reconditioner to further reduce the number of nonlinear iterations required.

Results are presented that demonstrate the improved accuracy offered by the new method when applied to several test problems. By successively

refining the meshes, it is also possible to demonstrate the increased order of the new method, when compared to a traditional shape function basedmethod. Comparing the resources required for both methods reveals that the new approach can be many times more efficient at producing a solution of a given accuracy.

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ID Code: 16303
Item Type: QUT Thesis (PhD)
Supervisor: Turner, Ian & Farrell, Troy
Keywords: Finite volume method, Diffusion, Advection, Radial basis functions, Gaussian quadrature, Control volume-finite element, Jacobian-free, Newton-Krylov, Unstructured mesh, Triangular mesh, Tetrahedral mesh, Parallelb preconditioner
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Department: Faculty of Science
Institution: Queensland University of Technology
Copyright Owner: Copyright Timothy John Moroney
Deposited On: 03 Dec 2008 04:00
Last Modified: 22 Feb 2013 02:57

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