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<p>Nonlinear coupled Boussinesq-type equations (NCBTEs) are widely employed to address wave resonance problems in ports. This study explores the application of nonlinear processes over varying bathymetry using Nwogu’s 2D depth-integrated NCBTEs for modeling shallow water wave propagation in coastal zones. A hybrid numerical scheme combining the finite volume method (FVM) and finite difference method (FDM) is employed to solve the governing equations (NCBTEs). The FVM is utilized to handle the conservative flux form of the NCBTEs, while the dispersive terms are treated using the FDM. The approach incorporates an approximate Riemann solver with Roe’s technique for advection and a well-balanced topography source term upwinding method for advection fluxes. Time integration of the 2D depth integrated NCBTEs evaluates the conserved variables, which is provide the valur of horizontal velocity components by systems of linear equations.The model is validated using analytical solutions for rectangular harbor oscillations, encompassing both linear and nonlinear cases. The accuracy of the numerical scheme is corroborated through prior numerical studies. This modeling technique offers practical implications for addressing wave motion problems in ocean engineering, particularly in the context of the Paradip Port in Odisha, India.</p>

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Nonlinear coupled 2D Boussinesq type equations for shallow water waves using finite volume finite difference methods

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Vinita,
  • Prashant Kumar,
  • Prachi Priya

摘要

Nonlinear coupled Boussinesq-type equations (NCBTEs) are widely employed to address wave resonance problems in ports. This study explores the application of nonlinear processes over varying bathymetry using Nwogu’s 2D depth-integrated NCBTEs for modeling shallow water wave propagation in coastal zones. A hybrid numerical scheme combining the finite volume method (FVM) and finite difference method (FDM) is employed to solve the governing equations (NCBTEs). The FVM is utilized to handle the conservative flux form of the NCBTEs, while the dispersive terms are treated using the FDM. The approach incorporates an approximate Riemann solver with Roe’s technique for advection and a well-balanced topography source term upwinding method for advection fluxes. Time integration of the 2D depth integrated NCBTEs evaluates the conserved variables, which is provide the valur of horizontal velocity components by systems of linear equations.The model is validated using analytical solutions for rectangular harbor oscillations, encompassing both linear and nonlinear cases. The accuracy of the numerical scheme is corroborated through prior numerical studies. This modeling technique offers practical implications for addressing wave motion problems in ocean engineering, particularly in the context of the Paradip Port in Odisha, India.