A Higher-order two-dimensional Boussinesq wave model

A two-dimensional Boussinesq-type model is presented accurate to O(μ)⁶ , μ = h₀/l₀, in dispersion and all consequential order for non-linearity with arbitrary bottom boundary, where h₀ is the water depth and l₀ is the characteristic wave length. The mathematical formulation is an extension of (4,4) the Padé approximant to include varying bottom boundary in two horizontal dimensions. A higher order perturbation method is used for mathematical derivation of the presented model. A two horizontal dimension numerical model is developed based on derived equations using the Finite Difference Method in higher-order scheme for time and space. The numerical wave model is verified successfully in several checks such as wave transition over an arbitrary bottom and the accuracy of numerical results in all cases are acceptable.