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Title: A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations
Authors: Ben Wongsaijai
Nattakorn Sukantamala
Kanyuta Poochinapan
Keywords: Mathematics
Issue Date: 1-Dec-2020
Abstract: © 2020, The Author(s). In the paper, a high-order alternating direction implicit (ADI) algorithm is presented to solve problems of unsteady convection and diffusion. The method is fourth- and second-order accurate in space and time, respectively. The resulting matrix at each ADI computation can be obtained by repeatedly solving a penta-diagonal system which produces a computationally cost-effective solver. We prove that the proposed scheme is mass-conserved and unconditionally stable by means of discrete Fourier analysis. Numerical experiments are performed to validate the mass conservation and illustrate that the proposed scheme is accurate and reliable for convection-dominated problems.
ISSN: 16871847
Appears in Collections:CMUL: Journal Articles

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