Development and application of a semi-analytical method with diagonal coefficient matrices for analysis of wave diffraction around vertical cylinders of arbitrary cross-sections

Abstract

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. In this method, only the boundaries of domain are discretized using special sub-parametric elements. The formulation of elements is constructed by employing higher-order Chebyshev mapping functions and special shape functions. 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. Furthermore, the first derivative of shape functions of any given control point are set to zero. 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. In other words, the governing equation for each degree of freedom (DOF) is independent of other DOFs of the domain. Accuracy and efficiency of present method are fully demonstrated through three short-crested wave diffraction problems which are successfully modeled using a few numbers of DOFs (or nodes), with excellent agreements between the results of the present method and those of other analytical/numerical solutions.