Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple the...Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.展开更多
Based on the screw theory and the driven-chain principle,a methodology of structural synthesis for fully-decoupled two-translational(2T) and two-rotational(2R) parallel mechanism is proposed by analyzing the character...Based on the screw theory and the driven-chain principle,a methodology of structural synthesis for fully-decoupled two-translational(2T) and two-rotational(2R) parallel mechanism is proposed by analyzing the characteristics of the input-output relations for fully-decoupled parallel mechanisms.Firstly,according to the desired kinematic characteristics of fully-decoupled parallel mechanisms,a method is proposed by virtue of screw theory to synthesize the desired forms for both the direct and the inverse Jacobian matrices.Secondly,according to the feature of the direct and the inverse Jacobian matrices,the effective screws,the actuated screws and the mobile un-actuated screws of each leg are established based on the reciprocal screw theory and all possible topology structures fulfilling the requirements are obtained.Finally,the desired fully-decoupled parallel mechanisms can be synthesized by using the structural synthesis rule and structural synthesis of fullydecoupled 2T2R parallel mechanisms can be obtained exploiting the abovementioned methodology.In particular,the direct Jacobian matrix of each synthesized fully-decoupled 2T2R parallel mechanism is a non-zero diagonal matrix throughout the entire workspace.Motors are mounted on each leg and each one of them actuates one degree-of-freedom(Do F) of the fully-decoupled parallel mechanism through a one-to-one velocity relation.展开更多
To avoid the existence of nonlinear and strong coupling in parallel mechanisms,it is necessary to address special care to the type synthesis of mechanisms,especially for the type synthesis of fully-decoupled parallel ...To avoid the existence of nonlinear and strong coupling in parallel mechanisms,it is necessary to address special care to the type synthesis of mechanisms,especially for the type synthesis of fully-decoupled parallel mechanisms. Based on the screw theory and the driven-chain principle,a methodology of structural synthesis for fully-decoupled three-rotational( 3R) and two-translational( 2T)parallel mechanisms was proposed by analyzing the characteristics of the input-output relations for fully-decoupled parallel mechanisms.Firstly,according to the desired kinematic characteristics of fullydecoupled parallel mechanisms,a method was presented by virtue of screw theory to synthesize the desired forms for both the direct and the inverse Jacobian matrices. Secondly,according to the feature of the direct and the inverse Jacobian matrices,the effective screws,the actuated screws and the mobile un-actuated screws of each leg were established based on the reciprocal screw theory and all possible topology structures fulfilling the requirements were obtained.Finally,the desired fully-decoupled parallel mechanisms could be synthesized by using the structural synthesis rule and structural synthesis of fully-decoupled 3R2 T parallel mechanisms could be obtained exploiting the abovementioned methodology. Furthermore,the Jacobian matrix of a synthesized 3R2 T parallel mechanism was deduced to demonstrate the decoupling feature of the parallel mechanism,which also validated the correctness of the methodology of the type synthesis for fully-decoupled 3R2 T parallel mechanisms.展开更多
基金supported by the NSFC Grant no.12271492the Natural Science Foundation of Henan Province of China Grant no.222300420550+1 种基金supported by the NSFC Grant no.12271498the National Key R&D Program of China Grant no.2022YFA1005202/2022YFA1005200.
文摘Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.
基金Sponsored by the National Natural Science Foundation of China(Grant No.50905075)the Open Project of the State Key Laboratory of Robotics and System(Grant No.SKLRS-2016-KF-06)+2 种基金the Open Project of the State Key Laboratory of Mechanical System and Vibration of China(Grant No.MSV201407)the Open Project of Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology(Grant No.FM-201402)the Research and the Innovation Project for College Graduates of Jiangsu Province(Grant No.SJZZ16-0212)
文摘Based on the screw theory and the driven-chain principle,a methodology of structural synthesis for fully-decoupled two-translational(2T) and two-rotational(2R) parallel mechanism is proposed by analyzing the characteristics of the input-output relations for fully-decoupled parallel mechanisms.Firstly,according to the desired kinematic characteristics of fully-decoupled parallel mechanisms,a method is proposed by virtue of screw theory to synthesize the desired forms for both the direct and the inverse Jacobian matrices.Secondly,according to the feature of the direct and the inverse Jacobian matrices,the effective screws,the actuated screws and the mobile un-actuated screws of each leg are established based on the reciprocal screw theory and all possible topology structures fulfilling the requirements are obtained.Finally,the desired fully-decoupled parallel mechanisms can be synthesized by using the structural synthesis rule and structural synthesis of fullydecoupled 2T2R parallel mechanisms can be obtained exploiting the abovementioned methodology.In particular,the direct Jacobian matrix of each synthesized fully-decoupled 2T2R parallel mechanism is a non-zero diagonal matrix throughout the entire workspace.Motors are mounted on each leg and each one of them actuates one degree-of-freedom(Do F) of the fully-decoupled parallel mechanism through a one-to-one velocity relation.
基金National Natural Science Foundation of China(No.50905075)the Six Talent Peaks Project in Jiangsu Province,China(No.ZBZZ-012)+4 种基金the Fundamental Research Funds for the Central Universities,China(No.JUSRP51316B)the Open Project of the State Key Laboratory of Mechanical System and Vibration of China(No.MSV201407)the Open Project of the Key Laboratory of System Control and Information Processing,China(No.Scip201506)the Open Project of Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology,China(No.FM-201402)the Research and the Innovation Project for College Graduates of Jiangsu Province,China(No.KYLX-1115)
文摘To avoid the existence of nonlinear and strong coupling in parallel mechanisms,it is necessary to address special care to the type synthesis of mechanisms,especially for the type synthesis of fully-decoupled parallel mechanisms. Based on the screw theory and the driven-chain principle,a methodology of structural synthesis for fully-decoupled three-rotational( 3R) and two-translational( 2T)parallel mechanisms was proposed by analyzing the characteristics of the input-output relations for fully-decoupled parallel mechanisms.Firstly,according to the desired kinematic characteristics of fullydecoupled parallel mechanisms,a method was presented by virtue of screw theory to synthesize the desired forms for both the direct and the inverse Jacobian matrices. Secondly,according to the feature of the direct and the inverse Jacobian matrices,the effective screws,the actuated screws and the mobile un-actuated screws of each leg were established based on the reciprocal screw theory and all possible topology structures fulfilling the requirements were obtained.Finally,the desired fully-decoupled parallel mechanisms could be synthesized by using the structural synthesis rule and structural synthesis of fully-decoupled 3R2 T parallel mechanisms could be obtained exploiting the abovementioned methodology. Furthermore,the Jacobian matrix of a synthesized 3R2 T parallel mechanism was deduced to demonstrate the decoupling feature of the parallel mechanism,which also validated the correctness of the methodology of the type synthesis for fully-decoupled 3R2 T parallel mechanisms.
