Implementation of a Second-Order TVD Transport Algorithm in the General Ocean Model (GOM)
This study presents the implementation of a scalar transport algorithm in the recently developed General Ocean Model (GOM), a three-dimensional, unstructured grid, finite volume/finite difference model. Solving the advection–diffusion transport equation is an essential part of any ocean circulation...
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MDPI AG
2025-06-01
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| Series: | Journal of Marine Science and Engineering |
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| Online Access: | https://www.mdpi.com/2077-1312/13/7/1296 |
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| author | Jungwoo Lee Jun Lee Sang-Leen Yun Seog-Ku Kim |
| author_facet | Jungwoo Lee Jun Lee Sang-Leen Yun Seog-Ku Kim |
| author_sort | Jungwoo Lee |
| collection | DOAJ |
| description | This study presents the implementation of a scalar transport algorithm in the recently developed General Ocean Model (GOM), a three-dimensional, unstructured grid, finite volume/finite difference model. Solving the advection–diffusion transport equation is an essential part of any ocean circulation model since the baroclinic density gradient distinguishes saline water from freshwater. To achieve both high accuracy and computational efficiency, we adopted a second-order semi-implicit Total Variation Diminishing (TVD) scheme. The TVD approach, known for its ability to suppress non-physical oscillations near steep gradients, provides a higher-fidelity representation of salinity fronts without introducing significant numerical artifacts. The TVD algorithm is constructed with the first-order Upwind scheme, which is known for suffering from excessive numerical diffusion, and the higher-order anti-diffusive flux term. The implemented transport algorithm is evaluated using two standard test cases, an ideal lock exchange problem and a U-shaped channel problem, and it is further applied to simulate salinity dynamics in Mobile Bay, Alabama. The model results from both the first-order Upwind and second-order TVD schemes are compared. The results indicate that the TVD scheme marginally improves the resolution of salinity fronts while maintaining computational stability and efficiency. The implementation enables a flexible and straightforward transition between the first-order scheme, which is faster than the second-order scheme, and the second-order scheme, which is less diffusive than the first-order scheme, enhancing the GOM’s capability for realistic and efficient salinity simulations in a tidally driven estuarine system. |
| format | Article |
| id | doaj-art-c60ea50ccea742a89efea8ce451346ed |
| institution | Matheson Library |
| issn | 2077-1312 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Marine Science and Engineering |
| spelling | doaj-art-c60ea50ccea742a89efea8ce451346ed2025-07-25T13:27:01ZengMDPI AGJournal of Marine Science and Engineering2077-13122025-06-01137129610.3390/jmse13071296Implementation of a Second-Order TVD Transport Algorithm in the General Ocean Model (GOM)Jungwoo Lee0Jun Lee1Sang-Leen Yun2Seog-Ku Kim3Department of Engineering, Faculty of Engineering, College of Engineering and Technology, East Carolina University, Greenville, NC 27858, USAKorea Coastal Ocean Modeling Solutions, Uiwang 16037, Republic of KoreaDepartment of Environmental Research, Korea Institute of Civil Engineering and Building Technology, Ilsanseo-gu, Goyang-si 10223, Republic of KoreaDepartment of Environmental Research, Korea Institute of Civil Engineering and Building Technology, Ilsanseo-gu, Goyang-si 10223, Republic of KoreaThis study presents the implementation of a scalar transport algorithm in the recently developed General Ocean Model (GOM), a three-dimensional, unstructured grid, finite volume/finite difference model. Solving the advection–diffusion transport equation is an essential part of any ocean circulation model since the baroclinic density gradient distinguishes saline water from freshwater. To achieve both high accuracy and computational efficiency, we adopted a second-order semi-implicit Total Variation Diminishing (TVD) scheme. The TVD approach, known for its ability to suppress non-physical oscillations near steep gradients, provides a higher-fidelity representation of salinity fronts without introducing significant numerical artifacts. The TVD algorithm is constructed with the first-order Upwind scheme, which is known for suffering from excessive numerical diffusion, and the higher-order anti-diffusive flux term. The implemented transport algorithm is evaluated using two standard test cases, an ideal lock exchange problem and a U-shaped channel problem, and it is further applied to simulate salinity dynamics in Mobile Bay, Alabama. The model results from both the first-order Upwind and second-order TVD schemes are compared. The results indicate that the TVD scheme marginally improves the resolution of salinity fronts while maintaining computational stability and efficiency. The implementation enables a flexible and straightforward transition between the first-order scheme, which is faster than the second-order scheme, and the second-order scheme, which is less diffusive than the first-order scheme, enhancing the GOM’s capability for realistic and efficient salinity simulations in a tidally driven estuarine system.https://www.mdpi.com/2077-1312/13/7/1296General Ocean Model (GOM)finite volumeunstructured gridtransport equationTVD schemeMobile Bay |
| spellingShingle | Jungwoo Lee Jun Lee Sang-Leen Yun Seog-Ku Kim Implementation of a Second-Order TVD Transport Algorithm in the General Ocean Model (GOM) Journal of Marine Science and Engineering General Ocean Model (GOM) finite volume unstructured grid transport equation TVD scheme Mobile Bay |
| title | Implementation of a Second-Order TVD Transport Algorithm in the General Ocean Model (GOM) |
| title_full | Implementation of a Second-Order TVD Transport Algorithm in the General Ocean Model (GOM) |
| title_fullStr | Implementation of a Second-Order TVD Transport Algorithm in the General Ocean Model (GOM) |
| title_full_unstemmed | Implementation of a Second-Order TVD Transport Algorithm in the General Ocean Model (GOM) |
| title_short | Implementation of a Second-Order TVD Transport Algorithm in the General Ocean Model (GOM) |
| title_sort | implementation of a second order tvd transport algorithm in the general ocean model gom |
| topic | General Ocean Model (GOM) finite volume unstructured grid transport equation TVD scheme Mobile Bay |
| url | https://www.mdpi.com/2077-1312/13/7/1296 |
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