In marine engineering,appendages such as fin stabilizers and/or T-foils are made to rotate and to reduce the motion of ships.Research on the hydrodynamics of ships fitted with active appendages has significantly impro...In marine engineering,appendages such as fin stabilizers and/or T-foils are made to rotate and to reduce the motion of ships.Research on the hydrodynamics of ships fitted with active appendages has significantly improved the design and control of such ships.However,most studies focus on fixed rather than rotating appendages,thereby ignoring the hydrodynamic unsteadiness of active appendages.To enhance the reliability and precision of the numerical simulations,we propose the use of overlapping grids for simulating advanced catamarans fitted with a pair of rotating T-foils under each bow.The fundamental purpose of the overlapping grid technique is to realize information exchange via regional overlap sharing in each subdomain of the computing domain,instead of using the method of boundary sharing,thus greatly alleviating the difficulty of generating the subdomain grid;moreover,the technique guarantees the quality of the subdomain grid.Within the main computational domain,a subdomain was allocated to accommodate the T-foil.Overlapping meshes near the interface between the two domains enable information flow during the simulation;the overlapping grids are updated at every iteration step because the subdomain rotates.The instantaneous trim and sinkage responses of the catamaran to the T-foil rotation were reproduced.From the moment the active T-foil stopped moving,there was no change in the ship’s sailing attitude,indicating that the response was in real time.By comparing with EFD data,the numerical results showed reasonable agreement,indicating the feasibility and effectiveness of the technique in simulating the hydrodynamics of ships fitted with active appendages.展开更多
A class of nonlinear parabolic equation on a polygonal domain Ω R2 is inves- tigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based o...A class of nonlinear parabolic equation on a polygonal domain Ω R2 is inves- tigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, we prove that the error of the discrete variational problem has good approximation properties. Our results are valid for any spatial dimensions. A numerical example to illustrate the theoretical results is also given.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.51509053)
文摘In marine engineering,appendages such as fin stabilizers and/or T-foils are made to rotate and to reduce the motion of ships.Research on the hydrodynamics of ships fitted with active appendages has significantly improved the design and control of such ships.However,most studies focus on fixed rather than rotating appendages,thereby ignoring the hydrodynamic unsteadiness of active appendages.To enhance the reliability and precision of the numerical simulations,we propose the use of overlapping grids for simulating advanced catamarans fitted with a pair of rotating T-foils under each bow.The fundamental purpose of the overlapping grid technique is to realize information exchange via regional overlap sharing in each subdomain of the computing domain,instead of using the method of boundary sharing,thus greatly alleviating the difficulty of generating the subdomain grid;moreover,the technique guarantees the quality of the subdomain grid.Within the main computational domain,a subdomain was allocated to accommodate the T-foil.Overlapping meshes near the interface between the two domains enable information flow during the simulation;the overlapping grids are updated at every iteration step because the subdomain rotates.The instantaneous trim and sinkage responses of the catamaran to the T-foil rotation were reproduced.From the moment the active T-foil stopped moving,there was no change in the ship’s sailing attitude,indicating that the response was in real time.By comparing with EFD data,the numerical results showed reasonable agreement,indicating the feasibility and effectiveness of the technique in simulating the hydrodynamics of ships fitted with active appendages.
基金Supported by the Natural Science Foundation of Hunan under Grant No. 06C713.
文摘A class of nonlinear parabolic equation on a polygonal domain Ω R2 is inves- tigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, we prove that the error of the discrete variational problem has good approximation properties. Our results are valid for any spatial dimensions. A numerical example to illustrate the theoretical results is also given.
