A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations
Abstract 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 rep...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02885-6 |
| _version_ | 1818843368502853632 |
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| author | Ben Wongsaijai Nattakorn Sukantamala Kanyuta Poochinapan |
| author_facet | Ben Wongsaijai Nattakorn Sukantamala Kanyuta Poochinapan |
| author_sort | Ben Wongsaijai |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-19T04:56:46Z |
| format | Article |
| id | doaj.art-068a48d28dc04248a4fdaec4b0753124 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-19T04:56:46Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-068a48d28dc04248a4fdaec4b07531242022-12-21T20:35:12ZengSpringerOpenAdvances in Difference Equations1687-18472020-09-012020112410.1186/s13662-020-02885-6A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equationsBen Wongsaijai0Nattakorn Sukantamala1Kanyuta Poochinapan2Advanced Research Center for Computational Simulation, Chiang Mai UniversityAdvanced Research Center for Computational Simulation, Chiang Mai UniversityAdvanced Research Center for Computational Simulation, Chiang Mai UniversityAbstract 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.http://link.springer.com/article/10.1186/s13662-020-02885-6Mass-conservativeHigh-order compact schemeUnsteady convection–diffusion equationAlternating direction implicit (ADI) method |
| spellingShingle | Ben Wongsaijai Nattakorn Sukantamala Kanyuta Poochinapan A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations Advances in Difference Equations Mass-conservative High-order compact scheme Unsteady convection–diffusion equation Alternating direction implicit (ADI) method |
| title | 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_short | 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 |
| topic | Mass-conservative High-order compact scheme Unsteady convection–diffusion equation Alternating direction implicit (ADI) method |
| url | http://link.springer.com/article/10.1186/s13662-020-02885-6 |
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