Mathematical Modeling of Two-Dimensional Depth Integrated Nonlinear Coupled Boussinesq-Type Equations for Shallow-Water Waves with Ship-Born Generation Waves in Coastal Regions
A hybrid computational framework integrating the finite volume method (FVM) and finite difference method (FDM) is developed to solve two-dimensional, time-dependent nonlinear coupled Boussinesq-type equations (NCBTEs) based on Nwogu’s depth-integrated formulation. This approach models nonlinear disp...
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MDPI AG
2025-03-01
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| author | Vinita Prashant Kumar |
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| description | A hybrid computational framework integrating the finite volume method (FVM) and finite difference method (FDM) is developed to solve two-dimensional, time-dependent nonlinear coupled Boussinesq-type equations (NCBTEs) based on Nwogu’s depth-integrated formulation. This approach models nonlinear dispersive wave forces acting on a stationary vessel and incorporates a frequency dispersion term to represent ship-wave generation due to a localized moving pressure disturbance. The computational domain is divided into two distinct regions: an inner domain surrounding the ship and an outer domain representing wave propagation. The inner domain is governed by the three-dimensional Laplace equation, accounting for the region beneath the ship and the confined space between the ship’s right side and a vertical quay wall. Conversely, the outer domain follows Nwogu’s 2D depth-integrated NCBTEs to describe water wave dynamics. Interface conditions are applied to ensure continuity by enforcing the conservation of volume flux and surface elevation matching between the two regions. The accuracy of this coupled numerical scheme is verified through convergence analysis, and its validity is established by comparing the simulation results with prior studies. Numerical experiments demonstrate the model’s capability to capture wave responses to simplified pressure disturbances and simulate wave propagation over intricate bathymetry. This computational framework offers an efficient and robust tool for analyzing nonlinear wave interactions with stationary ships or harbor structures. The methodology is specifically applied to examine the response of moored vessels to incident waves within Paradip Port, Odisha, India. |
| format | Article |
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| institution | DOAJ |
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| language | English |
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| series | Journal of Marine Science and Engineering |
| spelling | doaj-art-af16f0e09575422483e2e6266a8099af2025-08-20T02:42:34ZengMDPI AGJournal of Marine Science and Engineering2077-13122025-03-0113356210.3390/jmse13030562Mathematical Modeling of Two-Dimensional Depth Integrated Nonlinear Coupled Boussinesq-Type Equations for Shallow-Water Waves with Ship-Born Generation Waves in Coastal RegionsVinita0Prashant Kumar1Department of Applied Sciences, National Institute of Technology, Delhi 110036, IndiaDepartment of Applied Sciences, National Institute of Technology, Delhi 110036, IndiaA hybrid computational framework integrating the finite volume method (FVM) and finite difference method (FDM) is developed to solve two-dimensional, time-dependent nonlinear coupled Boussinesq-type equations (NCBTEs) based on Nwogu’s depth-integrated formulation. This approach models nonlinear dispersive wave forces acting on a stationary vessel and incorporates a frequency dispersion term to represent ship-wave generation due to a localized moving pressure disturbance. The computational domain is divided into two distinct regions: an inner domain surrounding the ship and an outer domain representing wave propagation. The inner domain is governed by the three-dimensional Laplace equation, accounting for the region beneath the ship and the confined space between the ship’s right side and a vertical quay wall. Conversely, the outer domain follows Nwogu’s 2D depth-integrated NCBTEs to describe water wave dynamics. Interface conditions are applied to ensure continuity by enforcing the conservation of volume flux and surface elevation matching between the two regions. The accuracy of this coupled numerical scheme is verified through convergence analysis, and its validity is established by comparing the simulation results with prior studies. Numerical experiments demonstrate the model’s capability to capture wave responses to simplified pressure disturbances and simulate wave propagation over intricate bathymetry. This computational framework offers an efficient and robust tool for analyzing nonlinear wave interactions with stationary ships or harbor structures. The methodology is specifically applied to examine the response of moored vessels to incident waves within Paradip Port, Odisha, India.https://www.mdpi.com/2077-1312/13/3/562nonlinear coupled Nwogu’s Boussinesq-type equationcoupled hybrid finite volume finite difference methodsolitary wavesregular waveswater wave propagation |
| spellingShingle | Vinita Prashant Kumar Mathematical Modeling of Two-Dimensional Depth Integrated Nonlinear Coupled Boussinesq-Type Equations for Shallow-Water Waves with Ship-Born Generation Waves in Coastal Regions Journal of Marine Science and Engineering nonlinear coupled Nwogu’s Boussinesq-type equation coupled hybrid finite volume finite difference method solitary waves regular waves water wave propagation |
| title | Mathematical Modeling of Two-Dimensional Depth Integrated Nonlinear Coupled Boussinesq-Type Equations for Shallow-Water Waves with Ship-Born Generation Waves in Coastal Regions |
| title_full | Mathematical Modeling of Two-Dimensional Depth Integrated Nonlinear Coupled Boussinesq-Type Equations for Shallow-Water Waves with Ship-Born Generation Waves in Coastal Regions |
| title_fullStr | Mathematical Modeling of Two-Dimensional Depth Integrated Nonlinear Coupled Boussinesq-Type Equations for Shallow-Water Waves with Ship-Born Generation Waves in Coastal Regions |
| title_full_unstemmed | Mathematical Modeling of Two-Dimensional Depth Integrated Nonlinear Coupled Boussinesq-Type Equations for Shallow-Water Waves with Ship-Born Generation Waves in Coastal Regions |
| title_short | Mathematical Modeling of Two-Dimensional Depth Integrated Nonlinear Coupled Boussinesq-Type Equations for Shallow-Water Waves with Ship-Born Generation Waves in Coastal Regions |
| title_sort | mathematical modeling of two dimensional depth integrated nonlinear coupled boussinesq type equations for shallow water waves with ship born generation waves in coastal regions |
| topic | nonlinear coupled Nwogu’s Boussinesq-type equation coupled hybrid finite volume finite difference method solitary waves regular waves water wave propagation |
| url | https://www.mdpi.com/2077-1312/13/3/562 |
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