A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity poten...A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.展开更多
To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed...To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.展开更多
A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both k...A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.展开更多
The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves.In the weakly non-linear assumption,the p...The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves.In the weakly non-linear assumption,the perturbation scheme is used and the expansion is conducted up to second-order to consider several non-linear quantities.To solve the boundary value problem,linearization is carried out based not on inertial coordinate but on body-fixed coordinate which could be accelerated by a motion of a body.At first,the main feature of the application of body-fixed coordinate system for a seakeeping problem is briefly described.After that the transformation of a coordinate system is extended to consider an elastic body motion and several physical variables are re-described in the generalized mode.It has been found that the deformation gradient could be used for the transformation of a coordinate system if several conditions are satisfied.Provided there are only vertical bending in elastic modes and the structure has relatively small depth,these conditions are generally satisfied.To calculate an elastic motion of a body,the generalized mode method is adopted and the mode shape is obtained by solving eigen-value problem of dynamic beam equation.In the boundary condition of the body-fixed coordinate system,the motion effect reflected to free-surface boundary is considered by extrapolating each mode shape to the horizontal direction from a body.At last,simple numerical tests are implemented as a validation process.The second-order hydrodynamic force of a freely floating hemisphere is first calculated in zero forward speed condition.Next,motion and added resistance of a ship with forward speed are considered at different flexibility to confirm the effect of an elastic body motion in body-fixed coordinate system.展开更多
基金financially supported by the National Natural Science Foundation of China (Grant Nos.52271276,52271319,and 52201364)the Natural Science Foundation of Jiangsu Province (Grant No.BK20201006)。
文摘A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.
基金Supported by the National Natural Science Foundation of China under (Grant No.107 72040,50709005 and 50921001)the Major National Science and Technology Projects of China under (Grant No.2008ZX05026-02)the Open Fund of State Key Laboratory of Ocean Engineering
文摘To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.
基金supported by the Fundamental Research Developing Association for Shipbuilding and Offshore (REDAS), Japan
文摘A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.
文摘The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves.In the weakly non-linear assumption,the perturbation scheme is used and the expansion is conducted up to second-order to consider several non-linear quantities.To solve the boundary value problem,linearization is carried out based not on inertial coordinate but on body-fixed coordinate which could be accelerated by a motion of a body.At first,the main feature of the application of body-fixed coordinate system for a seakeeping problem is briefly described.After that the transformation of a coordinate system is extended to consider an elastic body motion and several physical variables are re-described in the generalized mode.It has been found that the deformation gradient could be used for the transformation of a coordinate system if several conditions are satisfied.Provided there are only vertical bending in elastic modes and the structure has relatively small depth,these conditions are generally satisfied.To calculate an elastic motion of a body,the generalized mode method is adopted and the mode shape is obtained by solving eigen-value problem of dynamic beam equation.In the boundary condition of the body-fixed coordinate system,the motion effect reflected to free-surface boundary is considered by extrapolating each mode shape to the horizontal direction from a body.At last,simple numerical tests are implemented as a validation process.The second-order hydrodynamic force of a freely floating hemisphere is first calculated in zero forward speed condition.Next,motion and added resistance of a ship with forward speed are considered at different flexibility to confirm the effect of an elastic body motion in body-fixed coordinate system.
