Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

摘要

Highlights?A high-order finite-difference method is used to solve the forward-speed linearized radiation problem in time domain.?The overlapping body-fitted curvilinear grids together with the hyperbolic grid generation method are employed to represent the geometry of the body.?The numerical stability of the scheme is ensured by employing an upwind biased scheme for calculation of the convective derivatives at the free-surface conditions.?The method is validated by the reference solutions for the closed-form geometries, and also by the measurements for a bulk carrier ship geometry.AbstractThe linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability, the convective derivatives in the free-surface boundary conditions are treated using an upwind-biased stencil. Instead of solving for the radiation impulse response functions, a pseudo-impulsive Gaussian type displacement is employed in order to tailor the frequency-content to the discrete spatial resolution. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth-order convergence of the calculations on simple geometries is demonstrated, along with a nearly linear scaling of the solution effort with increasing grid resolution. The code is validated by comparison with analytical and semi-analytical solutions using submerged and floating closed-form geometries. Calculations are also made for a modern bulk carrier, and good agreement is found with experimental measurements.]]>