A mixed type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations
In this study, a mixed-type modal discontinuous Galerkin (DG) algorithm is utilized to simulate the nonlinear reaction-diffusion (RD) equations which describe miscellaneous physical phenomena involving in chemical processes, nuclear reactions, neutron multiplication etc. The current method is based...
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| Format: | Conference Paper |
| Language: | English |
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2022
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| Online Access: | https://hdl.handle.net/10356/156098 |
| _version_ | 1824455364257513472 |
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| author | Singh, Satyvir |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Singh, Satyvir |
| author_sort | Singh, Satyvir |
| collection | NTU |
| description | In this study, a mixed-type modal discontinuous Galerkin (DG) algorithm is utilized to simulate the nonlinear reaction-diffusion (RD) equations which describe miscellaneous physical phenomena involving in chemical processes, nuclear reactions, neutron multiplication etc. The current method is based on the concept of introducing an auxiliary unknown in the high-order derivative diffusion term. The third-order scaled Legendre polynomials are adopted for DG spatial discretization, while the third-order strong stability preserving (SSP) Runge-Kutta scheme is employed for a temporal marching algorithm. To verify the accuracy and reliability of the present DG scheme, three well-known numerical problems are solved. The present DG scheme yields the stable solutions and also shows a good choice to some substituting numerical schemes for approximating the nonlinear RD equations. |
| first_indexed | 2025-02-19T03:37:02Z |
| format | Conference Paper |
| id | ntu-10356/156098 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:37:02Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1560982023-02-28T19:18:01Z A mixed type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations Singh, Satyvir School of Physical and Mathematical Sciences International Conference on Advancements in Engineering and Sciences (ICAES2021) Science::Physics Nonlinear Reaction-Diffusion Equations Discontinuous Galerkin Algorithm In this study, a mixed-type modal discontinuous Galerkin (DG) algorithm is utilized to simulate the nonlinear reaction-diffusion (RD) equations which describe miscellaneous physical phenomena involving in chemical processes, nuclear reactions, neutron multiplication etc. The current method is based on the concept of introducing an auxiliary unknown in the high-order derivative diffusion term. The third-order scaled Legendre polynomials are adopted for DG spatial discretization, while the third-order strong stability preserving (SSP) Runge-Kutta scheme is employed for a temporal marching algorithm. To verify the accuracy and reliability of the present DG scheme, three well-known numerical problems are solved. The present DG scheme yields the stable solutions and also shows a good choice to some substituting numerical schemes for approximating the nonlinear RD equations. Published version 2022-11-15T07:26:14Z 2022-11-15T07:26:14Z 2022 Conference Paper Singh, S. (2022). A mixed type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations. International Conference on Advancements in Engineering and Sciences (ICAES2021), 2481, 040037-. https://dx.doi.org/10.1063/5.0103736 978-0-7354-4218-4 https://hdl.handle.net/10356/156098 10.1063/5.0103736 2481 040037 en © 2022 Author(s). Published by AIP Publishing. All rights reserved. This paper was published in AIP Conference Proceedings and is made available with permission of Author(s). application/pdf |
| spellingShingle | Science::Physics Nonlinear Reaction-Diffusion Equations Discontinuous Galerkin Algorithm Singh, Satyvir A mixed type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations |
| title | A mixed type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations |
| title_full | A mixed type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations |
| title_fullStr | A mixed type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations |
| title_full_unstemmed | A mixed type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations |
| title_short | A mixed type modal discontinuous Galerkin approach for solving nonlinear reaction diffusion equations |
| title_sort | mixed type modal discontinuous galerkin approach for solving nonlinear reaction diffusion equations |
| topic | Science::Physics Nonlinear Reaction-Diffusion Equations Discontinuous Galerkin Algorithm |
| url | https://hdl.handle.net/10356/156098 |
| work_keys_str_mv | AT singhsatyvir amixedtypemodaldiscontinuousgalerkinapproachforsolvingnonlinearreactiondiffusionequations AT singhsatyvir mixedtypemodaldiscontinuousgalerkinapproachforsolvingnonlinearreactiondiffusionequations |