The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical sym- metry properties of the numerical schemes are discus...The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical sym- metry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian （ALE） method. Numerical results are presented to compare three discrete configurations, i.e., the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometri- cal source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.展开更多
Rayleigh-Taylor instability of three fluid layers with two interfaces in cylindrical geometry is investigated analytically. The growth rates and the amplitudes of perturbation on the two interfaces are obtained. The f...Rayleigh-Taylor instability of three fluid layers with two interfaces in cylindrical geometry is investigated analytically. The growth rates and the amplitudes of perturbation on the two interfaces are obtained. The feedback factor from outer to inner interface is larger than that from inner to outer interface under the same conditions. The growth rate on the initially unstable interface is larger than the corresponding result in planar geometry for low mode perturbation. The two interfaces are decoupled for a larger mode number perturbation. The dependencies of the amplitudes of perturbation on different initial conditions are analyzed. The negative feedback effect from initially stable interface to another unstable interface is observed. In the limit of infinity inner radius and finite shell thickness, the results in planar geometry are recovered.展开更多
This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which ca...This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which can ensure the compatibility between edge fluxes and the nodal flow intrinsically.In two-dimensional cylindrical geometry,the control volume scheme and the area-weighted scheme are used respectively,which are distinguished by the discretizations for the source term in the momentum equation.The two-dimensional second-order extensions of these schemes are constructed by employing the monotone upwind scheme of conservation law(MUSCL)on unstructured meshes.Numerical results are provided to assess the robustness and accuracy of these new schemes.展开更多
The Rayleigh–Taylor instability（RTI） in cylindrical geometry is investigated analytically through a second-order weakly nonlinear（WN） theory considering the Bell–Plesset（BP） effect. The governing equations for...The Rayleigh–Taylor instability（RTI） in cylindrical geometry is investigated analytically through a second-order weakly nonlinear（WN） theory considering the Bell–Plesset（BP） effect. The governing equations for the combined perturbation growth are derived. The WN solutions for an exponentially convergent cylinder are obtained. It is found that the BP and RTI growths are strongly coupled, which results in the bubble-spike asymmetric structure in the WN stage. The large Atwood number leads to the large deformation of the convergent interface. The amplitude of the spike grows faster than that of the bubble especially for large mode number m and large Atwood number A. The averaged interface radius is small for large mode number perturbation due to the mode-coupling effect.展开更多
Rayleigh–Taylor instability(RTI)in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN)model.When the initial velocity perturb...Rayleigh–Taylor instability(RTI)in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN)model.When the initial velocity perturbation is comparable to the interface perturbation,the coupling between them plays a significant role.The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small.The effects of the mode number on the first three harmonics are discussed respectively.The low-mode number perturbation leads to large amplitudes of RTI growth.The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly.When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.展开更多
In this work,the effect of a magnetic island on Alfvén waves is studied.A physical model is established wherein Alfvén waves propagate in the presence of a magnetic island in a cylindrical geometry.The struc...In this work,the effect of a magnetic island on Alfvén waves is studied.A physical model is established wherein Alfvén waves propagate in the presence of a magnetic island in a cylindrical geometry.The structure of the Alfvén wave continuum is calculated by considering only the coupling caused by the periodicity in the helical angle of the magnetic island.The results show that the magnetic island can induce an upshift in the Alfvén continuum.Moreover,the coupling between different branches of the continuous spectrum becomes more significant with increasing continuum mode numbers near the boundary of the magnetic island.展开更多
We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry.The research is based on two-temperature models with Larsen’s f...We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry.The research is based on two-temperature models with Larsen’s flux-limited diffusion operators.Finite volume spatially discrete schemes are developed to circumvent the singularity at the origin and the polar axis and assure local conservation.Asymmetric second order accurate spatial approximation is utilized instead of the traditional first order one for boundary flux-limiters to consummate the schemes with higher order global consistency errors.The harmonic average approach in spherical geometry is analyzed,and its second order accuracy is demonstrated.By formal analysis,we prove these schemes and their corresponding fully discrete schemes with implicitly balanced and linearly implicit time evolutions have first order asymptoticpreserving properties.By designing associated manufactured solutions and reference solutions,we verify the desired performance of the fully discrete schemes with numerical tests,which illustrates quantitatively they are first order asymptotic-preserving and basically second order accurate,hence competent for simulations of both equilibrium and non-equilibrium radiation diffusion problems.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11471048 and U1630249)the Foundation of Chinese Academy of Engineering Physics(No.2014A0202010)the Foundation of Laboratory of Computational Physics(No.9140C690202140C69293)
文摘The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical sym- metry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian （ALE） method. Numerical results are presented to compare three discrete configurations, i.e., the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometri- cal source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11275031,11475034,11575033,and 11274026)the National Basic Research Program of China(Grant No.2013CB834100)
文摘Rayleigh-Taylor instability of three fluid layers with two interfaces in cylindrical geometry is investigated analytically. The growth rates and the amplitudes of perturbation on the two interfaces are obtained. The feedback factor from outer to inner interface is larger than that from inner to outer interface under the same conditions. The growth rate on the initially unstable interface is larger than the corresponding result in planar geometry for low mode perturbation. The two interfaces are decoupled for a larger mode number perturbation. The dependencies of the amplitudes of perturbation on different initial conditions are analyzed. The negative feedback effect from initially stable interface to another unstable interface is observed. In the limit of infinity inner radius and finite shell thickness, the results in planar geometry are recovered.
基金Project supported by the National Natural Science Foundation of China(U1630249,11971071,11971069,11871113)the Science Challenge Project(JCKY2016212A502)the Foundation of Laboratory of Computation Physics.
文摘This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which can ensure the compatibility between edge fluxes and the nodal flow intrinsically.In two-dimensional cylindrical geometry,the control volume scheme and the area-weighted scheme are used respectively,which are distinguished by the discretizations for the source term in the momentum equation.The two-dimensional second-order extensions of these schemes are constructed by employing the monotone upwind scheme of conservation law(MUSCL)on unstructured meshes.Numerical results are provided to assess the robustness and accuracy of these new schemes.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11275031,11475034,11575033 and 11274026the National Basic Research Program of China under Grant No 2013CB834100
文摘The Rayleigh–Taylor instability（RTI） in cylindrical geometry is investigated analytically through a second-order weakly nonlinear（WN） theory considering the Bell–Plesset（BP） effect. The governing equations for the combined perturbation growth are derived. The WN solutions for an exponentially convergent cylinder are obtained. It is found that the BP and RTI growths are strongly coupled, which results in the bubble-spike asymmetric structure in the WN stage. The large Atwood number leads to the large deformation of the convergent interface. The amplitude of the spike grows faster than that of the bubble especially for large mode number m and large Atwood number A. The averaged interface radius is small for large mode number perturbation due to the mode-coupling effect.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11275031,11475034,11575033,and 11274026)the National Basic Research Program of China(Grant No.2013CB834100)
文摘Rayleigh–Taylor instability(RTI)in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN)model.When the initial velocity perturbation is comparable to the interface perturbation,the coupling between them plays a significant role.The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small.The effects of the mode number on the first three harmonics are discussed respectively.The low-mode number perturbation leads to large amplitudes of RTI growth.The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly.When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.
基金supported by the ITER Project of Ministry of Science and Technology(No.2022YFE03080002)National Natural Science Foundation of China(Nos.11605088 and 12005100)+5 种基金the Key Scientific Research Program of Education Department of Hunan Province(Nos.20A417 and 20A439)the National Magnetic Confinement Fusion Science Program of China(No.2015GB110002)the Hunan Provincial Natural Science Foundation of China(No.2017JJ3268)the International Cooperation Base Project of Hunan Province of China(No.2018WK4009)the Key Laboratory of Magnetic Confinement Nuclear Fusion Research in Hengyang(No.2018KJ108)the PhD Start-Up Fund of University of South China(No.2017XQD08)。
文摘In this work,the effect of a magnetic island on Alfvén waves is studied.A physical model is established wherein Alfvén waves propagate in the presence of a magnetic island in a cylindrical geometry.The structure of the Alfvén wave continuum is calculated by considering only the coupling caused by the periodicity in the helical angle of the magnetic island.The results show that the magnetic island can induce an upshift in the Alfvén continuum.Moreover,the coupling between different branches of the continuous spectrum becomes more significant with increasing continuum mode numbers near the boundary of the magnetic island.
基金The authors are very grateful to the editors and the anonymous referees for helpful suggestions to enhance the paper.This work is supported by the National Natural Science Foundation of China(11271054,11471048,11571048,U1630249)the Science Foundation of CAEP(2014A0202010)the Science Challenge Project(No.JCKY2016212A502)and the Foundation of LCP.
文摘We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry.The research is based on two-temperature models with Larsen’s flux-limited diffusion operators.Finite volume spatially discrete schemes are developed to circumvent the singularity at the origin and the polar axis and assure local conservation.Asymmetric second order accurate spatial approximation is utilized instead of the traditional first order one for boundary flux-limiters to consummate the schemes with higher order global consistency errors.The harmonic average approach in spherical geometry is analyzed,and its second order accuracy is demonstrated.By formal analysis,we prove these schemes and their corresponding fully discrete schemes with implicitly balanced and linearly implicit time evolutions have first order asymptoticpreserving properties.By designing associated manufactured solutions and reference solutions,we verify the desired performance of the fully discrete schemes with numerical tests,which illustrates quantitatively they are first order asymptotic-preserving and basically second order accurate,hence competent for simulations of both equilibrium and non-equilibrium radiation diffusion problems.
