A remark on the invariant energy quadratization (IEQ) method for preserving the original energy dissipation laws
In this letter, we revisit the invariant energy quadratization (IEQ) method and provide a new perspective on its ability to preserve the original energy dissipation laws. The IEQ method has been widely used to design energy stable numerical schemes for phase-field or gradient flow models. Although t...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-02-01
|
| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022037?viewType=HTML |
| _version_ | 1811344196732190720 |
|---|---|
| author | Zengyan Zhang Yuezheng Gong Jia Zhao |
| author_facet | Zengyan Zhang Yuezheng Gong Jia Zhao |
| author_sort | Zengyan Zhang |
| collection | DOAJ |
| description | In this letter, we revisit the invariant energy quadratization (IEQ) method and provide a new perspective on its ability to preserve the original energy dissipation laws. The IEQ method has been widely used to design energy stable numerical schemes for phase-field or gradient flow models. Although there are many merits of the IEQ method, one major disadvantage is that the IEQ method usually respects a modified energy law, where the modified energy is expressed in the auxiliary variables. Still, the dissipation laws in terms of the original energy are not guaranteed by the IEQ method. Using the widely-used Cahn-Hilliard equation as an example, we demonstrate that the Runge-Kutta IEQ method indeed can preserve the original energy dissipation laws for certain situations up to arbitrary high-order accuracy. Interested readers are encouraged to extend this idea to more general cases and apply it to other thermodynamically consistent models. |
| first_indexed | 2024-04-13T19:43:29Z |
| format | Article |
| id | doaj.art-ba72fd55f6ff46a69cbcb333212872ab |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-13T19:43:29Z |
| publishDate | 2022-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-ba72fd55f6ff46a69cbcb333212872ab2022-12-22T02:32:48ZengAIMS PressElectronic Research Archive2688-15942022-02-0130270171410.3934/era.2022037A remark on the invariant energy quadratization (IEQ) method for preserving the original energy dissipation lawsZengyan Zhang0Yuezheng Gong1Jia Zhao21. Department of Mathematics & Statistics, Utah State University, Logan, UT 84322, USA2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China 3. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing 211106, China1. Department of Mathematics & Statistics, Utah State University, Logan, UT 84322, USAIn this letter, we revisit the invariant energy quadratization (IEQ) method and provide a new perspective on its ability to preserve the original energy dissipation laws. The IEQ method has been widely used to design energy stable numerical schemes for phase-field or gradient flow models. Although there are many merits of the IEQ method, one major disadvantage is that the IEQ method usually respects a modified energy law, where the modified energy is expressed in the auxiliary variables. Still, the dissipation laws in terms of the original energy are not guaranteed by the IEQ method. Using the widely-used Cahn-Hilliard equation as an example, we demonstrate that the Runge-Kutta IEQ method indeed can preserve the original energy dissipation laws for certain situations up to arbitrary high-order accuracy. Interested readers are encouraged to extend this idea to more general cases and apply it to other thermodynamically consistent models.https://www.aimspress.com/article/doi/10.3934/era.2022037?viewType=HTMLenergy stablecahn hilliard equationinvariant energy quadratization (ieq) method |
| spellingShingle | Zengyan Zhang Yuezheng Gong Jia Zhao A remark on the invariant energy quadratization (IEQ) method for preserving the original energy dissipation laws Electronic Research Archive energy stable cahn hilliard equation invariant energy quadratization (ieq) method |
| title | A remark on the invariant energy quadratization (IEQ) method for preserving the original energy dissipation laws |
| title_full | A remark on the invariant energy quadratization (IEQ) method for preserving the original energy dissipation laws |
| title_fullStr | A remark on the invariant energy quadratization (IEQ) method for preserving the original energy dissipation laws |
| title_full_unstemmed | A remark on the invariant energy quadratization (IEQ) method for preserving the original energy dissipation laws |
| title_short | A remark on the invariant energy quadratization (IEQ) method for preserving the original energy dissipation laws |
| title_sort | remark on the invariant energy quadratization ieq method for preserving the original energy dissipation laws |
| topic | energy stable cahn hilliard equation invariant energy quadratization (ieq) method |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022037?viewType=HTML |
| work_keys_str_mv | AT zengyanzhang aremarkontheinvariantenergyquadratizationieqmethodforpreservingtheoriginalenergydissipationlaws AT yuezhenggong aremarkontheinvariantenergyquadratizationieqmethodforpreservingtheoriginalenergydissipationlaws AT jiazhao aremarkontheinvariantenergyquadratizationieqmethodforpreservingtheoriginalenergydissipationlaws AT zengyanzhang remarkontheinvariantenergyquadratizationieqmethodforpreservingtheoriginalenergydissipationlaws AT yuezhenggong remarkontheinvariantenergyquadratizationieqmethodforpreservingtheoriginalenergydissipationlaws AT jiazhao remarkontheinvariantenergyquadratizationieqmethodforpreservingtheoriginalenergydissipationlaws |