Potential flow

Engineering

Boundary (topology)

Marine engineering

Boundary value problem

Applied mathematics

Singularity

Geology

Oceanography

Naval architecture

Thermodynamics

Physics

Finite element method

Quadrilateral

Mathematics

Hull

Mathematical analysis

Geometry

Boundary element method

Isogeometric analysis

Structural engineering

Mechanics

Piecewise

Basis function

Ocean Engineering

In the present work isogeometric analysis is applied to the solution of the boundary integral equation associated with the Neumann–Kelvin problem and the calculation of the wave resistance of ships. As opposed to low-order panel methods, where the body is represented by a large number of quadrilateral panels and the velocity potential is assumed to be piecewise constant (or approximated by low degree polynomials) on each panel, the isogeometric concept is based on exploiting the same NURBS basis, used for representing exactly the body geometry, for approximating the singularity distribution (and, in general, the dependent physical quantities). In order to examine the accuracy of the present method, numerical results obtained in the case of submerged and surface piercing bodies are compared against analytical solutions, experimental data and predictions provided by the low-order panel or other similar methods appeared in the pertinent literature, illustrating the superior efficiency of the isogeometric approach. The present approach by applying isogeometric analysis and boundary element method to the linear NK problem has the novelty of combining modern CAD systems for ship-hull design with computational hydrodynamics tools.

A BEM-isogeometric method for the ship wave-resistance problem