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 ...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.展开更多
A three-dimensional high-order panel method based on non-uniform rational B-spline(NURBS) is developed for predicting the hydrodynamic interaction forces on a moored ship induced by a passing ship in shallow water. An...A three-dimensional high-order panel method based on non-uniform rational B-spline(NURBS) is developed for predicting the hydrodynamic interaction forces on a moored ship induced by a passing ship in shallow water. An NURBS surface is used to precisely represent the hull geometry. Velocity potential on the hull surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to the boundary integral equation discretization. Under the assumption of low passing speed, the effect of free surface elevation is neglected in the numerical calculation, and infinite image method is used to deal with the finite water depth effect. The time stepping method is used to solve the velocity potential at each time step. Detailed convergence study with respect to time step, panel size and Green function is undertaken. The present results of hydrodynamic forces are compared with those obtained by slender-body theory to show the validity of the proposed numerical method. Calculations are conducted for different water depths and lateral distances between ships, and the detail results are presented to demonstrate the effects of these factors.展开更多
开发了一种基于B样条的高阶面元法用来求解浅水船舶兴波问题。船体表面和自由面上分别布置Rankine源,同时利用镜像原理来计及水底的影响。物体几何用 B 样条曲面精确表示。在求得边界面上的源强密度分布后,物面上的速度势用B样条来表示...开发了一种基于B样条的高阶面元法用来求解浅水船舶兴波问题。船体表面和自由面上分别布置Rankine源,同时利用镜像原理来计及水底的影响。物体几何用 B 样条曲面精确表示。在求得边界面上的源强密度分布后,物面上的速度势用B样条来表示。数值计算中采用配置方法,并且用高斯—勒让德公式来计算方程中的积分。为了验证文中方法的有效性,用本方法计算了Wigley船在深水和浅水中的兴波水动力和波形,所得数值结果与试验结果和其它数值结果进行了比较,吻合程度令人满意,表明本方法被用来求解浅水船舶兴波问题是有效的。展开更多
A 3D rankine panel method was developed for calculating the linear wave-making resistance of a tri-maran with Wigley hulls. In order to calculate the normal vector and derivative of the body surface accurately, non-un...A 3D rankine panel method was developed for calculating the linear wave-making resistance of a tri-maran with Wigley hulls. In order to calculate the normal vector and derivative of the body surface accurately, non-uniform rational B-spline (NURBS) was adopted to represent body surface and rankine source density. The radiation condition is satisfied using the numerical technology of staggered grids. Numerical results show that the linear wave-making resistance of the trimaran can be calculated effectively using this method.展开更多
基金supported by the National Natural SciencFoundation of China (Grant No. 10572094)the NaturScience Foundation of Shanghai (Grant No. 06ZR14050)
文摘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.
基金the National Natural Science Foundation of China(Nos.51179019 and 51309152)
文摘A three-dimensional high-order panel method based on non-uniform rational B-spline(NURBS) is developed for predicting the hydrodynamic interaction forces on a moored ship induced by a passing ship in shallow water. An NURBS surface is used to precisely represent the hull geometry. Velocity potential on the hull surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to the boundary integral equation discretization. Under the assumption of low passing speed, the effect of free surface elevation is neglected in the numerical calculation, and infinite image method is used to deal with the finite water depth effect. The time stepping method is used to solve the velocity potential at each time step. Detailed convergence study with respect to time step, panel size and Green function is undertaken. The present results of hydrodynamic forces are compared with those obtained by slender-body theory to show the validity of the proposed numerical method. Calculations are conducted for different water depths and lateral distances between ships, and the detail results are presented to demonstrate the effects of these factors.
基金Supported by the Special Research Fund for the Doctoral Program of Higher Education (GrantNo. 20050248037)the National Natural Science Foundation of China (Grant No. 10572094)
基金Supported by the National Natural Science Foundation of China (Grant No: 10572094)the Natural Science Foundation of Shanghai (Grant No: 06ZR14050)
文摘开发了一种基于B样条的高阶面元法用来求解浅水船舶兴波问题。船体表面和自由面上分别布置Rankine源,同时利用镜像原理来计及水底的影响。物体几何用 B 样条曲面精确表示。在求得边界面上的源强密度分布后,物面上的速度势用B样条来表示。数值计算中采用配置方法,并且用高斯—勒让德公式来计算方程中的积分。为了验证文中方法的有效性,用本方法计算了Wigley船在深水和浅水中的兴波水动力和波形,所得数值结果与试验结果和其它数值结果进行了比较,吻合程度令人满意,表明本方法被用来求解浅水船舶兴波问题是有效的。
基金the National Natural Science Founda-tion of China (No. 10572094)the Special ResearchFund for the Doctoral Program of Higher Education(No. 20050248037)
文摘A 3D rankine panel method was developed for calculating the linear wave-making resistance of a tri-maran with Wigley hulls. In order to calculate the normal vector and derivative of the body surface accurately, non-uniform rational B-spline (NURBS) was adopted to represent body surface and rankine source density. The radiation condition is satisfied using the numerical technology of staggered grids. Numerical results show that the linear wave-making resistance of the trimaran can be calculated effectively using this method.
