TheMoon is the only celestial body that human beings have visited.The design of the Earth-Moon transfer orbits is a critical issue in lunar exploration missions.In the 21st century,new lunar missions including the con...TheMoon is the only celestial body that human beings have visited.The design of the Earth-Moon transfer orbits is a critical issue in lunar exploration missions.In the 21st century,new lunar missions including the construction of the lunar space station,the permanent lunar base,and the Earth-Moon transportation network have been proposed,requiring low-cost,expansive launch windows and a fixed arrival epoch for any launch date within the launch window.The low-energy and low-thrust transfers are promising strategies to satisfy the demands.This review provides a detailed landscape of Earth-Moon transfer trajectory design processes,from the traditional patched conic to the state-of-the-art low-energy and low-thrust methods.Essential mechanisms of the various utilized dynamic models and the characteristics of the different design methods are discussed in hopes of helping readers grasp thebasic overviewof the current Earth-Moon transfer orbitdesignmethods anda deep academic background is unnecessary for the context understanding.展开更多
In this paper, we study the problem of boundary layer for nonstationary flows of viscous incompressible fluids. There are some open problems in the field of boundary layer. The method used here is mainly based on a tr...In this paper, we study the problem of boundary layer for nonstationary flows of viscous incompressible fluids. There are some open problems in the field of boundary layer. The method used here is mainly based on a transformation which reduces the boundary layer system to an initial-boundary value problem for a single quasilinear parabolic equation. We prove the existence of weak solutions to the modified nonstationary boundary layer system. Moreover, the stability and uniqueness of weak solutions are discussed.展开更多
In this article,we study the system w让h boundary degeneracy wit-div(a(x)|s■ui|Pi^-2■ui)=fi(x,t,u1,u2),(x,t)∈T.Applying the monotone iterattion technique and the regularization method,we get the existence of soluti...In this article,we study the system w让h boundary degeneracy wit-div(a(x)|s■ui|Pi^-2■ui)=fi(x,t,u1,u2),(x,t)∈T.Applying the monotone iterattion technique and the regularization method,we get the existence of solution for a regularized system.Moreover,under an integral condition on the coefficient function a(x),the existence and the uniqueness of the local solutions of the system is obtained by using a standard limiting process.Finally,the stability of the solutions is proved without any boundary value cond让ion,provided a(x)satisfies another restriction.展开更多
A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boun...A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boundary procedure is applied near boundaries in an extended domain where data is known.We show how to raise the order of accuracy of the scheme,how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries.The new boundary procedure is cheap,easy to implement and suitable for all numerical methods,not only finite difference methods,that employ weak boundary conditions.Numerical results that corroborate the analysis are presented.展开更多
A conforming discontinuous Galerkinfinite element method was introduced by Ye and Zhang,on simplicial meshes and on polytopal meshes,which has theflexibility of using discontinuous approximation and an ultra simple form...A conforming discontinuous Galerkinfinite element method was introduced by Ye and Zhang,on simplicial meshes and on polytopal meshes,which has theflexibility of using discontinuous approximation and an ultra simple formulation.The main goal of this paper is to improve the above discontinuous Galerkinfinite element method so that it can handle nonhomogeneous Dirichlet boundary conditions effectively.In addition,the method has been generalized in terms of approximation of the weak gradient.Error estimates of optimal order are established for the correspond-ing discontinuousfinite element approximation in both a discrete H1 norm and the L2 norm.Numerical results are presented to confirm the theory.展开更多
基金supported by the National Key Research and Development Program of China(No.2021YFA0717100)the National Natural Science Foundation of China(Nos.12072270 and U2013206).
文摘TheMoon is the only celestial body that human beings have visited.The design of the Earth-Moon transfer orbits is a critical issue in lunar exploration missions.In the 21st century,new lunar missions including the construction of the lunar space station,the permanent lunar base,and the Earth-Moon transportation network have been proposed,requiring low-cost,expansive launch windows and a fixed arrival epoch for any launch date within the launch window.The low-energy and low-thrust transfers are promising strategies to satisfy the demands.This review provides a detailed landscape of Earth-Moon transfer trajectory design processes,from the traditional patched conic to the state-of-the-art low-energy and low-thrust methods.Essential mechanisms of the various utilized dynamic models and the characteristics of the different design methods are discussed in hopes of helping readers grasp thebasic overviewof the current Earth-Moon transfer orbitdesignmethods anda deep academic background is unnecessary for the context understanding.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10131050).
文摘In this paper, we study the problem of boundary layer for nonstationary flows of viscous incompressible fluids. There are some open problems in the field of boundary layer. The method used here is mainly based on a transformation which reduces the boundary layer system to an initial-boundary value problem for a single quasilinear parabolic equation. We prove the existence of weak solutions to the modified nonstationary boundary layer system. Moreover, the stability and uniqueness of weak solutions are discussed.
基金The paper is supported by Natural Science Foundation of Fujian province in China(no:2019J01858).
文摘In this article,we study the system w让h boundary degeneracy wit-div(a(x)|s■ui|Pi^-2■ui)=fi(x,t,u1,u2),(x,t)∈T.Applying the monotone iterattion technique and the regularization method,we get the existence of solution for a regularized system.Moreover,under an integral condition on the coefficient function a(x),the existence and the uniqueness of the local solutions of the system is obtained by using a standard limiting process.Finally,the stability of the solutions is proved without any boundary value cond让ion,provided a(x)satisfies another restriction.
基金supported by the National Science Foundation under Award No.0948304 and by the Southern California Earthquake Center.SCEC is funded by NSF Cooperative Agreement EAR-0529922 and USGS Cooperative Agreement 07HQAG0008(SCEC contribution number 1806).The work by the last author was carried out within the Swedish e-science Research Centre(SeRC)and supported by the Swedish Research Council(VR).
文摘A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boundary procedure is applied near boundaries in an extended domain where data is known.We show how to raise the order of accuracy of the scheme,how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries.The new boundary procedure is cheap,easy to implement and suitable for all numerical methods,not only finite difference methods,that employ weak boundary conditions.Numerical results that corroborate the analysis are presented.
基金supported in part by National Natural Science Foundation of China(NSFC No.11871038)supported in part by National Science Foundation Grant DMS-1620016.
文摘A conforming discontinuous Galerkinfinite element method was introduced by Ye and Zhang,on simplicial meshes and on polytopal meshes,which has theflexibility of using discontinuous approximation and an ultra simple formulation.The main goal of this paper is to improve the above discontinuous Galerkinfinite element method so that it can handle nonhomogeneous Dirichlet boundary conditions effectively.In addition,the method has been generalized in terms of approximation of the weak gradient.Error estimates of optimal order are established for the correspond-ing discontinuousfinite element approximation in both a discrete H1 norm and the L2 norm.Numerical results are presented to confirm the theory.
