The Higher Order Derivatives Calculations Of Velocity Potential Based On B-spline Theory

When considering the problem of a ship advancing in waves by using multi domain Rankine-Kelvin sources method, the fluid domain is divided into two subdomains by a control surface, combining Kelvin source method with the Rankine panel method. Across the control surface both the velocity potential and its normal derivative are to be continuous. However,due to the complex boundary condition on the free surface, the integral equation involves not only the unknown velocity potential but also its first-order and second-order derivatives on the free surface. It is difficult to solve the integral equation with differential terms. Therefore,this thesis is very meaningful in the research of high order derivative calculations of the velocity potential based on the B spline theory.Firstly, the background of this thesis is introduced briefly: the integral equation could not be solved containing the high order derivative of the velocity potential. through the mathematical description of the multi domain Rankine-Kelvin method and the derivation and simplification of the formula .It is concluded that the study of high order derivatives calculations of velocity potential is of great significance.Subsequently, the basic theory of B -Spline curves and surface including parametrization method, reverse calculation method and node vector calculation method is detailed introduced.Then the program which is used for B-spline panel generation of arbitrary three-dimensional shapes is developed and has laid a foundation for further study.Lastly, it is put forward a program to calculate high order derivatives of velocity potential on the wall and free surface. Four numerical examples are given to indicate the feasibility of the algorithm and the optimization of the grid partition method makes it possible to reach higher accuracy. It is signality in solving the hydrodynamic problem of floating body by using multi domain Rankine-Kelvin method.