A two-parameter Serre–Green–Naghdi model with optimized linear dispersion

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This study presents an improved two-parameter Serre–Green–Naghdi (iSGN) model with enhanced linear dispersion properties. Two independent parameters are introduced into the non-hydrostatic pressure closure and optimized to match the exact Airy-wave dispersion relation, reducing the maximum phase speed error from about 20% in the classical formulation to 3.57% for μ ≤ π (with only 0.39% error at μ = 2.5 ). The modified equations retain the original two-equation structure and full nonlinearity. A hybrid finite-volume/finite-difference scheme is used for discretization, with mass conservation ensured by the finite-volume treatment of the continuity equation. At the open boundaries, an Orlanski-type radiation boundary condition is implemented, in which the local phase speed is dynamically evaluated from the interior flow solution to suppress spurious reflections. Validation against Gaussian wave packet propagation and wave transformation over a submerged bar confirms the model’s improved dispersion accuracy and performance over variable bathymetry. A systematic shoaling analysis reveals that the [ 0 / 2 ] Padé-type models, including the present iSGN formulation, share a common deep-water shoaling limit of γ s = − 1 / 10 , which is a structural limitation independent of parameter optimization. This highlights the inherent trade-off between dispersion accuracy and shoaling consistency in Boussinesq-type equations.