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An efficient HOC scheme for transient convection‐diffusion‐reaction equations with discontinuous coefficients and singular source terms
Author(s) -
Ray Rajendra K,
Kalita Jiten C,
Dass Anoop K
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700967
Subject(s) - discontinuity (linguistics) , convection–diffusion equation , transient (computer programming) , grid , space (punctuation) , diffusion , convection , mathematics , mathematical analysis , computer science , mechanics , physics , geometry , thermodynamics , operating system
In this paper, we propose a new methodology for numerically solving one‐dimensional (1D) transient convection‐diffusion‐reaction equations with discontinuous coefficients and singular source terms on nonuniform space grids. This Higher Order Compact (HOC) formulation is at least third order accurate at regular grid points and exactly third order accurate at points just next to the discontinuity. We conduct numerous numerical studies on a number of problems and compare our results with those obtained with immersed interface and other well‐known methods. In all cases our formulation is found to produce better results on relatively coarser grids. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)