A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations
© 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 o...
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th-cmuir.6653943832-706912020-10-14T08:39:29Z A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations Ben Wongsaijai Nattakorn Sukantamala Kanyuta Poochinapan Mathematics © 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. 2020-10-14T08:39:29Z 2020-10-14T08:39:29Z 2020-12-01 Journal 16871847 16871839 2-s2.0-85091307728 10.1186/s13662-020-02885-6 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85091307728&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/70691 |
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Mathematics Ben Wongsaijai Nattakorn Sukantamala Kanyuta Poochinapan A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations |
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© 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. |
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Journal |
author |
Ben Wongsaijai Nattakorn Sukantamala Kanyuta Poochinapan |
author_facet |
Ben Wongsaijai Nattakorn Sukantamala Kanyuta Poochinapan |
author_sort |
Ben Wongsaijai |
title |
A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations |
title_short |
A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations |
title_full |
A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations |
title_fullStr |
A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations |
title_full_unstemmed |
A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations |
title_sort |
mass-conservative higher-order adi method for solving unsteady convection–diffusion equations |
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2020 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85091307728&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/70691 |
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