Efficient Implicit-Explicit Time Stepping for Accurate and Rapid Simulation of Chromatographic Models

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

In this paper, we give a summary of recent advances (K. Meyer et al, 2018) on the use of a nodal discontinuous Galerkin finite element (DG-FE) method for spatial discretization of chromatographic models. Explicit Runge-Kutta (ERK) methods are popular for integrating the semi-discrete systems of equations resulting from DG space discretization. However, ERK methods suffer from stability-based time step restrictions for stiff problems. Therefore, we implement a high order implicit-explicit additive Runge-Kutta (IMEX-ARK) method (Kennedy and Carpenter, 2003, 2007) to overcome system stiffness. The IMEX-RK method advances the non-stiff parts of the model using explicit methods and solve the more expensive stiff parts using an L-stable stiffly-accurate explicit, singly diagonally implicit Runge-Kutta method (ESDIRK). We show that for a multicomponent nonlinear chromatographic system, the IMEX-ARK scheme becomes more efficient than explicit methods for increasingly stiff systems. We recommend integrating the convective term using explicit methods and to integrate both the diffusive and reactive terms using implicit methods.
Original languageEnglish
Title of host publicationProceedings of the 13th International Symposium on Process Systems Engineering – PSE 2018
PublisherElsevier
Publication date2018
Pages853-858
ISBN (Electronic)978-0-444-64241-7
DOIs
Publication statusPublished - 2018
Event13th International Symposium on Process Systems Engineering (PSE 2018) - San DIego, United States
Duration: 1 Jul 20185 Jul 2018

Conference

Conference13th International Symposium on Process Systems Engineering (PSE 2018)
CountryUnited States
CitySan DIego
Period01/07/201805/07/2018
SeriesComputer Aided Chemical Engineering
ISSN1570-7946

Keywords

  • Langmuir isotherm
  • Nonlinear chromatography
  • High-order
  • Discontinuous Galerkin finite element method
  • Implicit-explicit

Cite this

Meyer, K., Huusom, J. K., & Abildskov, J. (2018). Efficient Implicit-Explicit Time Stepping for Accurate and Rapid Simulation of Chromatographic Models. In Proceedings of the 13th International Symposium on Process Systems Engineering – PSE 2018 (pp. 853-858). Elsevier. Computer Aided Chemical Engineering https://doi.org/10.1016/B978-0-444-64241-7.50137-3
Meyer, Kristian ; Huusom, Jakob K. ; Abildskov, Jens. / Efficient Implicit-Explicit Time Stepping for Accurate and Rapid Simulation of Chromatographic Models. Proceedings of the 13th International Symposium on Process Systems Engineering – PSE 2018. Elsevier, 2018. pp. 853-858 (Computer Aided Chemical Engineering).
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abstract = "In this paper, we give a summary of recent advances (K. Meyer et al, 2018) on the use of a nodal discontinuous Galerkin finite element (DG-FE) method for spatial discretization of chromatographic models. Explicit Runge-Kutta (ERK) methods are popular for integrating the semi-discrete systems of equations resulting from DG space discretization. However, ERK methods suffer from stability-based time step restrictions for stiff problems. Therefore, we implement a high order implicit-explicit additive Runge-Kutta (IMEX-ARK) method (Kennedy and Carpenter, 2003, 2007) to overcome system stiffness. The IMEX-RK method advances the non-stiff parts of the model using explicit methods and solve the more expensive stiff parts using an L-stable stiffly-accurate explicit, singly diagonally implicit Runge-Kutta method (ESDIRK). We show that for a multicomponent nonlinear chromatographic system, the IMEX-ARK scheme becomes more efficient than explicit methods for increasingly stiff systems. We recommend integrating the convective term using explicit methods and to integrate both the diffusive and reactive terms using implicit methods.",
keywords = "Langmuir isotherm, Nonlinear chromatography, High-order, Discontinuous Galerkin finite element method, Implicit-explicit",
author = "Kristian Meyer and Huusom, {Jakob K.} and Jens Abildskov",
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Meyer, K, Huusom, JK & Abildskov, J 2018, Efficient Implicit-Explicit Time Stepping for Accurate and Rapid Simulation of Chromatographic Models. in Proceedings of the 13th International Symposium on Process Systems Engineering – PSE 2018. Elsevier, Computer Aided Chemical Engineering, pp. 853-858, 13th International Symposium on Process Systems Engineering (PSE 2018), San DIego, United States, 01/07/2018. https://doi.org/10.1016/B978-0-444-64241-7.50137-3

Efficient Implicit-Explicit Time Stepping for Accurate and Rapid Simulation of Chromatographic Models. / Meyer, Kristian; Huusom, Jakob K.; Abildskov, Jens.

Proceedings of the 13th International Symposium on Process Systems Engineering – PSE 2018. Elsevier, 2018. p. 853-858 (Computer Aided Chemical Engineering).

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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N2 - In this paper, we give a summary of recent advances (K. Meyer et al, 2018) on the use of a nodal discontinuous Galerkin finite element (DG-FE) method for spatial discretization of chromatographic models. Explicit Runge-Kutta (ERK) methods are popular for integrating the semi-discrete systems of equations resulting from DG space discretization. However, ERK methods suffer from stability-based time step restrictions for stiff problems. Therefore, we implement a high order implicit-explicit additive Runge-Kutta (IMEX-ARK) method (Kennedy and Carpenter, 2003, 2007) to overcome system stiffness. The IMEX-RK method advances the non-stiff parts of the model using explicit methods and solve the more expensive stiff parts using an L-stable stiffly-accurate explicit, singly diagonally implicit Runge-Kutta method (ESDIRK). We show that for a multicomponent nonlinear chromatographic system, the IMEX-ARK scheme becomes more efficient than explicit methods for increasingly stiff systems. We recommend integrating the convective term using explicit methods and to integrate both the diffusive and reactive terms using implicit methods.

AB - In this paper, we give a summary of recent advances (K. Meyer et al, 2018) on the use of a nodal discontinuous Galerkin finite element (DG-FE) method for spatial discretization of chromatographic models. Explicit Runge-Kutta (ERK) methods are popular for integrating the semi-discrete systems of equations resulting from DG space discretization. However, ERK methods suffer from stability-based time step restrictions for stiff problems. Therefore, we implement a high order implicit-explicit additive Runge-Kutta (IMEX-ARK) method (Kennedy and Carpenter, 2003, 2007) to overcome system stiffness. The IMEX-RK method advances the non-stiff parts of the model using explicit methods and solve the more expensive stiff parts using an L-stable stiffly-accurate explicit, singly diagonally implicit Runge-Kutta method (ESDIRK). We show that for a multicomponent nonlinear chromatographic system, the IMEX-ARK scheme becomes more efficient than explicit methods for increasingly stiff systems. We recommend integrating the convective term using explicit methods and to integrate both the diffusive and reactive terms using implicit methods.

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Meyer K, Huusom JK, Abildskov J. Efficient Implicit-Explicit Time Stepping for Accurate and Rapid Simulation of Chromatographic Models. In Proceedings of the 13th International Symposium on Process Systems Engineering – PSE 2018. Elsevier. 2018. p. 853-858. (Computer Aided Chemical Engineering). https://doi.org/10.1016/B978-0-444-64241-7.50137-3