Compact higher-order(HO)schemes for a new finite difference method,referred to as the Cartesian cut-stencil FD method,for the numerical solution of the convection-diffusion equation in complex shaped domains have been...Compact higher-order(HO)schemes for a new finite difference method,referred to as the Cartesian cut-stencil FD method,for the numerical solution of the convection-diffusion equation in complex shaped domains have been addressed in this paper.The Cartesian cut-stencil FD method,which employs 1-D quadratic transformation functions to map a non-uniform(uncut or cut)physical stencil to a uniform computational stencil,can be combined with compact HO Pad´e-Hermitian formulations to produce HO cut-stencil schemes.The modified partial differential equation technique is used to develop formulas for the local truncation error for the cut-stencil HO formulations.The effect of various HO approximations for Neumann boundary conditions on the solution accuracy and global order of convergence are discussed.The numerical results for second-order and compact HO formulations of the Cartesian cut-stencil FD method have been compared for test problems using the method of manufactured solutions.展开更多
A Time-domain Higher-Order Boundary Element Method（THOBEM） is developed for simulating wave-current interactions with 3-D floating bodies.Through a Taylor series expansion and a perturbation procedure,the model is f...A Time-domain Higher-Order Boundary Element Method（THOBEM） is developed for simulating wave-current interactions with 3-D floating bodies.Through a Taylor series expansion and a perturbation procedure,the model is formulated to the first-order in the wave steepness and in the current velocity,respectively.The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem.Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching.An artificial damping layer is adopted to dissipate the scattering waves.Different from the other time-domain numerical models,which are often focused on the wave-current interaction with restrained bodies,the present model deals with a floating hemisphere.The numerical results of wave forces,wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods.The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry.In this work,the regular and focused wave combined with current interacting with a truss-spar platform is investigated.展开更多
A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simp...A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.展开更多
A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constan...A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constant forward speed in incident waves and the resultant diffraction forces acting on the hull are computed to investigate the hull-form effects on the hydrodynamic forces. A rectangular computational domain travelling at ship＇s speed is considered. An artificial damping beach for satisfying the radiation condition is installed at the outer portion of the free surface except the downstream side. An iterative time-marching scheme is employed for updating both kinematic and dynamic free-surface boundary conditions for numerical accuracy and stability. The boundary integral equation is solved by distributing higher-order boundary elements over the wetted body surface and the free surface. The hull-form effects on the naval hydrodynamics are investigated by comparing three different Wigley models. Finally, the corresponding unsteady wave patterns and the wave profiles around the hulls are illustrated and discussed.展开更多
基金support from the Natural Sciences and Engineering Research Council of Canada through the Discovery Grants program.
文摘Compact higher-order(HO)schemes for a new finite difference method,referred to as the Cartesian cut-stencil FD method,for the numerical solution of the convection-diffusion equation in complex shaped domains have been addressed in this paper.The Cartesian cut-stencil FD method,which employs 1-D quadratic transformation functions to map a non-uniform(uncut or cut)physical stencil to a uniform computational stencil,can be combined with compact HO Pad´e-Hermitian formulations to produce HO cut-stencil schemes.The modified partial differential equation technique is used to develop formulas for the local truncation error for the cut-stencil HO formulations.The effect of various HO approximations for Neumann boundary conditions on the solution accuracy and global order of convergence are discussed.The numerical results for second-order and compact HO formulations of the Cartesian cut-stencil FD method have been compared for test problems using the method of manufactured solutions.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10772040, 50709005 and 5092100)the Important National Science and Technology Specific Projects of China (Grant No. 2008ZX05026-02)the Open Fund of Stabe Key Laboratory of Sabllite Ocean Environment Dynamics (Grant No. SOED1002)
文摘A Time-domain Higher-Order Boundary Element Method（THOBEM） is developed for simulating wave-current interactions with 3-D floating bodies.Through a Taylor series expansion and a perturbation procedure,the model is formulated to the first-order in the wave steepness and in the current velocity,respectively.The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem.Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching.An artificial damping layer is adopted to dissipate the scattering waves.Different from the other time-domain numerical models,which are often focused on the wave-current interaction with restrained bodies,the present model deals with a floating hemisphere.The numerical results of wave forces,wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods.The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry.In this work,the regular and focused wave combined with current interacting with a truss-spar platform is investigated.
文摘A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.
基金Project supported by the National Natural Science Foun-dation of China(Grant Nos.51579058,11502059)the Shandong Provincial Natural Science Foundation(Grant No.ZR2014EEQ016)
文摘A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constant forward speed in incident waves and the resultant diffraction forces acting on the hull are computed to investigate the hull-form effects on the hydrodynamic forces. A rectangular computational domain travelling at ship＇s speed is considered. An artificial damping beach for satisfying the radiation condition is installed at the outer portion of the free surface except the downstream side. An iterative time-marching scheme is employed for updating both kinematic and dynamic free-surface boundary conditions for numerical accuracy and stability. The boundary integral equation is solved by distributing higher-order boundary elements over the wetted body surface and the free surface. The hull-form effects on the naval hydrodynamics are investigated by comparing three different Wigley models. Finally, the corresponding unsteady wave patterns and the wave profiles around the hulls are illustrated and discussed.
