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A mapped-stencil finite difference scheme for the convection-diffusion equation on an arbitrary mesh

Barron, RM and Balasubramaniam, A (2020) A mapped-stencil finite difference scheme for the convection-diffusion equation on an arbitrary mesh. In: AIP Conference Proceedings, 23-28 September 2019, Sheraton Rhodes Resort Rhodes; Greece.

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Official URL: https://dx.doi.org/10.1063/5.0028532


A new finite difference methodology has been developed for the numerical solution of partial differential equations arising in multiphysics applications on complex domains. The mapped-stencil finite difference method presented in this research is based on a unique transformation which maps each 7-point stencil in the 3D physical domain to a generic uniform computational stencil on which the differential equations are discretized. The mesh can be of any type, or the domain may be covered by a cloud of points, as long as a stencil connectivity can be established for each node in the mesh. Hence, the restriction of finite difference methods to structured grids is eliminated. This new formulation is validated against analytical solutions and other simulation results, for a variety of unsteady and steady problems. © 2020 American Institute of Physics Inc.. All rights reserved.

Item Type: Conference Paper
Publication: AIP Conference Proceedings
Publisher: American Institute of Physics Inc.
Additional Information: cited By 0; Conference of International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 ; Conference Date: 23 September 2019 Through 28 September 2019; Conference Code:165330
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 11 Feb 2021 10:13
Last Modified: 11 Feb 2021 10:13
URI: http://eprints.iisc.ac.in/id/eprint/67530

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