On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(<i>β</i>-alanine)-Electrolyte
Three-component systems of diffusion–reaction equations play a central role in the modelling and simulation of chemical processes in engineering, electro-chemistry, physical chemistry, biology, population dynamics, etc. A major question in the simulation of three-component systems is how to guarante...
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| Format: | Article |
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MDPI AG
2021-03-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/14/4/113 |
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| author | Stephan Daniel Schwoebel Thomas Mehner Thomas Lampke |
| author_facet | Stephan Daniel Schwoebel Thomas Mehner Thomas Lampke |
| author_sort | Stephan Daniel Schwoebel |
| collection | DOAJ |
| description | Three-component systems of diffusion–reaction equations play a central role in the modelling and simulation of chemical processes in engineering, electro-chemistry, physical chemistry, biology, population dynamics, etc. A major question in the simulation of three-component systems is how to guarantee non-negative species distributions in the model and how to calculate them effectively. Current numerical methods to enforce non-negative species distributions tend to be cost-intensive in terms of computation time and they are not robust for big rate constants of the considered reaction. In this article, a method, as a combination of homotopy methods, modern augmented Lagrangian methods, and adaptive FEMs is outlined to obtain a robust and efficient method to simulate diffusion–reaction models with non-negative concentrations. Although in this paper the convergence analysis is not described rigorously, multiple numerical examples as well as an application to elctro-deposition from an aqueous <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>Cu</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula>-(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-alanine) electrolyte are presented. |
| first_indexed | 2024-03-10T12:46:18Z |
| format | Article |
| id | doaj.art-38c13ffb312143d5b559be0fc3efa270 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T12:46:18Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-38c13ffb312143d5b559be0fc3efa2702023-11-21T13:28:34ZengMDPI AGAlgorithms1999-48932021-03-0114411310.3390/a14040113On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(<i>β</i>-alanine)-ElectrolyteStephan Daniel Schwoebel0Thomas Mehner1Thomas Lampke2Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, GermanyMaterials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, GermanyMaterials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, GermanyThree-component systems of diffusion–reaction equations play a central role in the modelling and simulation of chemical processes in engineering, electro-chemistry, physical chemistry, biology, population dynamics, etc. A major question in the simulation of three-component systems is how to guarantee non-negative species distributions in the model and how to calculate them effectively. Current numerical methods to enforce non-negative species distributions tend to be cost-intensive in terms of computation time and they are not robust for big rate constants of the considered reaction. In this article, a method, as a combination of homotopy methods, modern augmented Lagrangian methods, and adaptive FEMs is outlined to obtain a robust and efficient method to simulate diffusion–reaction models with non-negative concentrations. Although in this paper the convergence analysis is not described rigorously, multiple numerical examples as well as an application to elctro-deposition from an aqueous <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>Cu</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula>-(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-alanine) electrolyte are presented.https://www.mdpi.com/1999-4893/14/4/113diffusion–reaction systemaugmented lagrangian methodadaptive FEMlaminar diffusion boundary layerthree-component systemcomplexation of metal ions |
| spellingShingle | Stephan Daniel Schwoebel Thomas Mehner Thomas Lampke On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(<i>β</i>-alanine)-Electrolyte Algorithms diffusion–reaction system augmented lagrangian method adaptive FEM laminar diffusion boundary layer three-component system complexation of metal ions |
| title | On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(<i>β</i>-alanine)-Electrolyte |
| title_full | On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(<i>β</i>-alanine)-Electrolyte |
| title_fullStr | On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(<i>β</i>-alanine)-Electrolyte |
| title_full_unstemmed | On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(<i>β</i>-alanine)-Electrolyte |
| title_short | On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(<i>β</i>-alanine)-Electrolyte |
| title_sort | on a robust and efficient numerical scheme for the simulation of stationary 3 component systems with non negative species concentration with an application to the cu deposition from a cu i β i alanine electrolyte |
| topic | diffusion–reaction system augmented lagrangian method adaptive FEM laminar diffusion boundary layer three-component system complexation of metal ions |
| url | https://www.mdpi.com/1999-4893/14/4/113 |
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