![]() ![]() By implementing weighted residual method and using Clenshaw–Curtis numerical integration, the coefficient matrices of equations system become diagonal, yielding a set of decoupled governing Bessel differential equations for the whole system. Furthermore, the first derivative of shape functions of any given control point are set to zero. The shape functions are introduced to satisfy Kronecker Delta property for the potential function and its derivative, corresponding to the governing Helmholtz equation of the problem. The formulation of elements is constructed by employing higher-order Chebyshev mapping functions and special shape functions. In this method, only the boundaries of domain are discretized using special sub-parametric elements. This paper proposes a semi-analytical method for modeling short-crested wave diffraction around a vertical cylinder of arbitrary cross-section, in an unbounded domain. The results were compared with experimental data, analytical solutions and other numerical methods, and reasonable agreements have been achieved. To evaluate the accuracy and capability of the proposed scheme for MSE, a series of numerical tests were conducted, covering a range of complexity that included propagation and transformation of waves due to a parabolic shoal, a circular island mounted on a paraboloidal shoal and elliptic shoal situated on a slope, as well as breakwater gap. The partial differential terms of the MSE for each point in the computational domain can be discretized into linear combinations of nearby function values with the moving-least-squares method of the GFDM, so the numerical implementation is very convenient and efficient. As a newly-developed domain-type meshless method, the GFDM can truly get rid of time-consuming meshing generation and numerical quadrature. In this paper, a meshless numerical algorithm, based on the generalized finite difference method (GFDM), is firstly proposed to efficiently and accurately solve the MSE. The mild slope equation (MSE) has been widely used to describe combined wave refraction and diffraction in the field of coastal and offshore engineering owing to its applicability for a wide range of wave frequencies. Thus, the current numerical model can be utilized efficiently for redesigning and constructing artificial ports or harbors in the coastal regions with variable bathymetries. Finally, the current numerical model is applied on a realistic Pohang New Harbor (PNH) under the resonance conditions. The amplification factor is obtained for T-shaped and TT-shaped domain to analyze the resonance modes. The numerical validation is conducted by the comparison of simulation results with analytical approximations and convergence analysis for the rectangular domain is also obtained. Hybrid mesh elements is considered for bounded region to enhance the numerical accuracy. Further, an analytical approach is utilized in an unbounded region based on Fourier bessel series solution of scattered waves. The solution of the mild slope equation is obtained in the bounded region with the consideration of variable bathymetry and partially reflected boundary using Hybrid element method. The domain of interest is divided in two regions as bounded and unbounded region. The resonant frequencies are estimated in PNH and Paradip port for the safe navigation of moored ship.Īn efficient numerical model is constructed with the combination of analytical and Hybrid Finite Element Method (HFEM) based on mild slope equation for shallow water waves to analyze the wave induced oscillation in an irregular geometrical domain. In addition, the spectral density is also determined for multidirectional random waves propagating towards the PNH and Paradip port at the same record station. The wave amplification is obtained at six record stations inside the PNH, South Korea and Paradip port, Odisha, India. Further, the simulation results are validated with BEM, analytical method and experimental data from Lee (1971) and Ippen and Goda (1963). Convergence analysis is performed on rectangular domain for present scheme, BEM and hybrid finite element method (HFEM), which shows that the present numerical scheme is better as compared to other traditional numerical schemes. The boundary Integrals are transformed using Jacobians and evaluated with Clenshaw Curtis Quadrature rule. The numerical solution on each boundary element is obtained by using boundary integral associated with Chebyshev point discretization. In SBEM, the boundary element method (BEM) is coupled with the spectral element method (SEM) to enhance the numerical accuracy of the present numerical scheme. A novel mathematical model formulation based on spectral boundary element method (SBEM) is presented to examine the wave response in the Pohang New Harbor (PNH), South Korea and Paradip port, Odisha, India. ![]()
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