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From discretization to regularization of composite discontinuous functions

Alsoudani, TM; Bogle, IDL; (2014) From discretization to regularization of composite discontinuous functions. Computers & Chemical Engineering , 62 139 - 160. 10.1016/j.compchemeng.2013.11.019. Green open access

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Abstract

Discontinuities between distinct regions, described by different equation sets, cause difficulties for PDE/ODE solvers. We present a new algorithm that eliminates integrator discontinuities through regularizing discontinuities. First, the algorithm determines the optimum switch point between two functions spanning adjacent or overlapping domains. The optimum switch point is determined by searching for a “jump point” that minimizes a discontinuity between adjacent/overlapping functions. Then, discontinuity is resolved using an interpolating polynomial that joins the two discontinuous functions. This approach eliminates the need for conventional integrators to either discretize and then link discontinuities through generating interpolating polynomials based on state variables or to reinitialize state variables when discontinuities are detected in an ODE/DAE system. In contrast to conventional approaches that handle discontinuities at the state variable level only, the new approach tackles discontinuity at both state variable and the constitutive equations level. Thus, this approach eliminates errors associated with interpolating polynomials generated at a state variable level for discontinuities occurring in the constitutive equations. Computer memory space requirements for this approach exponentially increase with the dimension of the discontinuous function hence there will be limitations for functions with relatively high dimensions. Memory availability continues to increase with price decreasing so this is not expected to be a major limitation.

Type: Article
Title: From discretization to regularization of composite discontinuous functions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.compchemeng.2013.11.019
Publisher version: http://dx.doi.org/10.1016/j.compchemeng.2013.11.01...
Language: English
Additional information: This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > VP: Research
URI: https://discovery.ucl.ac.uk/id/eprint/1469013
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