A hermite radial basis functions control volume numerical method to simulate transport problems

Orsini, Paolo (2009) A hermite radial basis functions control volume numerical method to simulate transport problems. PhD thesis, University of Nottingham.

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Abstract

This thesis presents a Control Volume (CV) method for transient transport problems where the cell surface fluxes are reconstructed using local interpolation functions that besides interpolating the nodal values of the field variable, also satisfies the governing equation at some auxiliary points in the interpolation stencils. The interpolation function relies on a Hermitian Radial Basis Function (HRBF) mesh less collocation approach to find the solution of auxiliary local boundary/initial value problems, which are solved using the same time integration scheme adopted to update the global control volume solution. By the use of interpolation functions that approximate the governing equation, a form of analytical upwinding scheme is achieved without the need of using predefined interpolation stencils according to the magnitude and direction of the local advective velocity. In this way, the interpolation formula retains the desired information about the advective velocity field, allowing the use of centrally defined stencils even in the case of advective dominant problems. This new CV approach, which is referred to as the CV-HRBF method, is applied to a series of transport problems characterised by high Peclet number.

This method is also more flexible than the classical CV formulations because the boundary conditions are explicitly imposed in the interpolation formula, without the need for artificial schemes (e.g. utilising dummy cells). The flexibility of the local meshless character of the CVHRBF is shown in the modelling of the saturated zone of the unconfined aquifer where a mesh adapting algorithm is needed to track the phreatic surface (moving boundary). Due to the use of a local RBF interpolation, the dynamic boundary condition can be applied in an arbitrary number of points on the phreatic surface, independently from the mesh element.

The robustness of the Hermite interpolation is exploited to formulate a non-overlapping non-iterative multi-domain scheme where physical matching conditions are satisfied locally, i.e. imposing the continuity of the function and flux at the sub-domain interface.

Item Type: Thesis (University of Nottingham only) (PhD) Power, H.Morvan, H.P. Groundwater flow, mathematical models, computational fluid dynamics, radial basis functions T Technology > TC Hydraulic engineering. Ocean engineering UK Campuses > Faculty of Engineering > Department of Mechanical, Materials and Manufacturing Engineering 28464 Airey, Ms Valerie 02 Mar 2015 09:28 12 Oct 2017 19:05 http://eprints.nottingham.ac.uk/id/eprint/28464

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