A THREE-DIMENSIONAL DESINGULARIZED HIGH ORDER PANEL METHOD BASED ON NURBS

A desingularized high order panel method based on Non-Uniform Rational B-Spline （NURBS） was developed to deal with three-dimensional potential flow problems. A NURBS surface was used to precisely represent the body geometry. Velocity potential on the body surface was described by the B-spline after the source density distribution on the body surface had been solved. The collocation approach was employed to satisfy the Neurnann boundary condition and Gaussian quadrature points were chosen as both the collocation points and the source points. The singularity was removed by a combined method, so the process of the numerical computation was non-singular. In order to verify the method proposed, the unbounded flow problems of sphere and ellipsoid, the wave-making problem of a submerged ellipsoid were chosen as computational examples. It is shown that the numerical results are in good agreement with analytical solutions and other numerical results in all cases, and sufficient accuracy of numerical solution can be reached with a small number of panels.

FULLY NONLINEAR WAVE COMPUTATIONS FOR ARBITRARY FLOATING BODIES USING THE DELTA METHOD

Fully nonlinear water wave problems are solved using Eulerian-Lagrangian timestepping methods in conjunction with a desingularized approach to solve the mixed boundary valueproblem that arises at each time step. In the desingularized approach, the singularities generatingthe flow field are outside the fluid domain. This allows the singularity distribution to be replacedby isolated Rankine sources with the corresponding reduction in computational complexity andcomputer time. A moving boundary technique is applied to e-liminate the reflection waves fromlimited computational boundaries. Examples of the use of the method in three-dimensions are givenfor the exciting forces acting on a modified wigley hull and Series 60 are presented. The numericalresults show good agreements with those of experiments.

An Improved Formulation of Singular Boundary Method

This study proposes a new formulation of singular boundary method(SBM)to solve the 2D potential problems,while retaining its original merits being free of integration and mesh,easy-to-program,accurate and mathematically simple without the requirement of a fictitious boundary as in the method of fundamental solutions(MFS).The key idea of the SBM is to introduce the concept of the origin intensity factor to isolate the singularity of fundamental solution so that the source points can be placed directly on the physical boundary.This paper presents a new approach to derive the analytical solution of the origin intensity factor based on the proposed subtracting and adding-back techniques.And the troublesome sample nodes in the ordinary SBM are avoided and the sample solution is also not necessary for the Neumann boundary condition.Three benchmark problems are tested to demonstrate the feasibility and accuracy of the new formulation through detailed comparisons with the boundary element method(BEM),MFS,regularized meshless method(RMM)and boundary distributed source(BDS)method.

Index Computations in FJRW Theory

We compute the index of the real Cauchy–Riemann operator defined in FJRW theory in case of the smooth metric.For the cylindrical metric,we study the relation between the index of the linearized operator of Witten map and weights in weighted Sobolev spaces.

Desingularized boundary integral equations and their applications in wave dynamics and wave-body interaction problems

Over the past 30 years or so,desingularized boundary integral equations(DBIEs)have been used to study water wave dynamics and body motion dynamics.Within the potential flow modeling,unlike conventional boundary integral methods,a DBIE separates the integration surface and the control(collocation)surface,resulting in a BIE with non-singular kernels.The desingularization allows simpler and faster numerical evaluation of the boundary integrals,and consequently faster numerical solutions.In this paper,derivations of different forms of DBIEs are given and the fundamental aspects and advantages of the DBIEs are reviewed and discussed.Numerical examples of applications of DBIEs in wave dynamics and body motion dynamics are given and the outlook of future development of the desingularized methods is discussed.