Numerical simulations of unsteady flow problems with moving boundaries commonly require the use of geometric conservation law(GCL).However,in cases of unidirectional large mesh deformation,the cumulative error caused ...Numerical simulations of unsteady flow problems with moving boundaries commonly require the use of geometric conservation law(GCL).However,in cases of unidirectional large mesh deformation,the cumulative error caused by the discrete procedure in GCL can significantly increase,and a direct consequence is that the calculated cell volume may become negative.To control the cumulative error,a new discrete GCL(D-GCL)is proposed.Unlike the original D-GCL,the proposed method uses the control volume analytically evaluated according to the grid motion at the time level n,instead of using the calculated value from the D-GCL itself.Error analysis indicates that the truncation error of the numerical scheme is guaranteed to be the same order as that obtained from the original D-GCL,while the accumulated error is greatly reduced.For validation,two challenging large deformation cases including a rotating circular cylinder case and a descending GAW-(1)two-element airfoil case are selected to be investigated.Good agreements are found between the calculated results and some other literature data,demonstrating the feasibility of the proposed D-GCL for unidirectional motions with large displacements.展开更多
In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is ...In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.展开更多
Based on newly developed weight-based smoothness detectors and non-linear interpolations designed to capture discontinuities for the multiderivative com-bined dissipative compact scheme(MDCS),hybrid linear and nonline...Based on newly developed weight-based smoothness detectors and non-linear interpolations designed to capture discontinuities for the multiderivative com-bined dissipative compact scheme(MDCS),hybrid linear and nonlinear interpolations are proposed to form hybrid MDCS.These detectors are derived from the weights used for the nonlinear interpolations and can provide suitable switches between the linear and the nonlinear schemes to realize the characteristics for the hybrid MDCS of capturing discontinuities and maintaining high resolution in the region without large discontinuities.To save computational cost,the nonlinear scheme with characteris-tic decomposition is only applied in the detected discontinuities region by specially designed hybrid strategy.Typical tests show that the hybrid MDCS is capable of cap-turing discontinuities and maintaining high resolution power for the smooth region at the same time.With the satisfaction of the geometric conservative law(GCL),the MDCS is further applied on curvilinear mesh to present its promising capability of handling pragmatic simulations.展开更多
We define a kind of KdV （Korteweg-de Vries） geometric flow for maps from a real line or a circle into a Kahler manifold （N,J,h） with complex structure J and metric h as the generalization of the vortex filament dy...We define a kind of KdV （Korteweg-de Vries） geometric flow for maps from a real line or a circle into a Kahler manifold （N,J,h） with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By using the geometric analysis, the existence of the Cauchy problems of the KdV geometric flows will be investigated in this note.展开更多
A manifestly covariant, or geometric, field theory of relativistic classical particle-field systems is devel- oped. The connection between the space-time symmetry and energy-momentum conservation laws of the system is...A manifestly covariant, or geometric, field theory of relativistic classical particle-field systems is devel- oped. The connection between the space-time symmetry and energy-momentum conservation laws of the system is established geometrically without splitting the space and time coordinates; i.e., space- time is treated as one entity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that the particles and the field reside on different manifolds. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of the electromagnetic fields and also a functional of the particles＇ world lines. The other difficulty associated with the geometric setting results from the mass-shell constraint. The standard Euler-Lagrange （EL） equation for a particle is generalized into the geometric EL equation when the mass-shell constraint is imposed. For the particle-field system, the geometric EL equation is further generalized into a weak geometric EL equation for particles. With the EL equation for the field and the geometric weak EL equation for particles, the symmetries and conservation laws can be established geometrically. A geometric expression for the particle energy-momentum tensor is derived for the first time, which recovers the non-geometric form in the literature for a chosen coordinate system.展开更多
Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study.High resolution has been achieved by Dissipative Compact Schemes(DCS),however,acco...Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study.High resolution has been achieved by Dissipative Compact Schemes(DCS),however,according to the recent research,applications of DCS on complex geometry may have serious problem for that the Geometric Conservation Law(GCL)is not satisfied,and this may cause numerical instability.To cope with this problem,a new scheme named Hybrid cell-edge and cell-node Dissipative Compact Scheme(HDCS)has been formulated.The formulation of the HDCS contains two steps.First,a new central compact scheme is formulated for the purpose of conveniently fulfilling the GCL,and then dissipation is added on the central scheme by high-order dissipative interpolation of cell-edge variables.The solutions of Euler and Navier-Stokes equations show that the HDCS can be applied successfully on complex geometry,while the DCS may suffer numerical instabilities.Moreover,high resolution of the HDCS may be observed in the test of scattering of acoustic waves by multiple cylinders.展开更多
基金supported by the National Basic Research Program of China(″973″Project)(No.2014CB046200)
文摘Numerical simulations of unsteady flow problems with moving boundaries commonly require the use of geometric conservation law(GCL).However,in cases of unidirectional large mesh deformation,the cumulative error caused by the discrete procedure in GCL can significantly increase,and a direct consequence is that the calculated cell volume may become negative.To control the cumulative error,a new discrete GCL(D-GCL)is proposed.Unlike the original D-GCL,the proposed method uses the control volume analytically evaluated according to the grid motion at the time level n,instead of using the calculated value from the D-GCL itself.Error analysis indicates that the truncation error of the numerical scheme is guaranteed to be the same order as that obtained from the original D-GCL,while the accumulated error is greatly reduced.For validation,two challenging large deformation cases including a rotating circular cylinder case and a descending GAW-(1)two-element airfoil case are selected to be investigated.Good agreements are found between the calculated results and some other literature data,demonstrating the feasibility of the proposed D-GCL for unidirectional motions with large displacements.
基金supported by National Natural Science Foundation of China(No.12005141)supported by National Natural Science Foundation of China(No.11805273)+2 种基金supported by the Collaborative Innovation Program of Hefei Science Center,CAS(No.2021HSCCIP019)National MC Energy R&D Program(No.2018YFE0304100)National Natural Science Foundation of China(No.11905220)。
文摘In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.
基金supported by the National Key Research and Development Plan(grant No.2016YFB0200700)the National Natural Science Foundation of China(grant Nos.11372342,11572342,and 11672321)the National Key Project GJXM92579.
文摘Based on newly developed weight-based smoothness detectors and non-linear interpolations designed to capture discontinuities for the multiderivative com-bined dissipative compact scheme(MDCS),hybrid linear and nonlinear interpolations are proposed to form hybrid MDCS.These detectors are derived from the weights used for the nonlinear interpolations and can provide suitable switches between the linear and the nonlinear schemes to realize the characteristics for the hybrid MDCS of capturing discontinuities and maintaining high resolution in the region without large discontinuities.To save computational cost,the nonlinear scheme with characteris-tic decomposition is only applied in the detected discontinuities region by specially designed hybrid strategy.Typical tests show that the hybrid MDCS is capable of cap-turing discontinuities and maintaining high resolution power for the smooth region at the same time.With the satisfaction of the geometric conservative law(GCL),the MDCS is further applied on curvilinear mesh to present its promising capability of handling pragmatic simulations.
文摘We define a kind of KdV （Korteweg-de Vries） geometric flow for maps from a real line or a circle into a Kahler manifold （N,J,h） with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By using the geometric analysis, the existence of the Cauchy problems of the KdV geometric flows will be investigated in this note.
基金This research was supported by the Na- tional Magnetic Confinement Fusion Energy Research Project （Grant Nos. 2015GB111003 and 2014GB124005）, the National Natural Science Foundation of China （Grant Nos. NSFC- 11575185, 11575186, and 11305171）, JSPS-NRF-NSFC A3 Fore- sight Program （Grant No. 11261140328）, the Key Research Pro- gram of Frontier Sciences CAS （QYZDB-SSW-SYS004）, Geo- Algorithmic Plasma Simulator （GAPS） Project, and the National Magnetic Confinement Fusion Energy Research Project （Grant No. 2013GB111002B）.
文摘A manifestly covariant, or geometric, field theory of relativistic classical particle-field systems is devel- oped. The connection between the space-time symmetry and energy-momentum conservation laws of the system is established geometrically without splitting the space and time coordinates; i.e., space- time is treated as one entity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that the particles and the field reside on different manifolds. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of the electromagnetic fields and also a functional of the particles＇ world lines. The other difficulty associated with the geometric setting results from the mass-shell constraint. The standard Euler-Lagrange （EL） equation for a particle is generalized into the geometric EL equation when the mass-shell constraint is imposed. For the particle-field system, the geometric EL equation is further generalized into a weak geometric EL equation for particles. With the EL equation for the field and the geometric weak EL equation for particles, the symmetries and conservation laws can be established geometrically. A geometric expression for the particle energy-momentum tensor is derived for the first time, which recovers the non-geometric form in the literature for a chosen coordinate system.
基金supported by the National Basic Research Program of China(Grant no.2009CB723800)National Natural Science Foundation of China(Grand Nos.11072259 and 11202226)the Foundation of State Key Laboratory of Aerodynamics(Grand Nos.JBKY11030902 and JBKY11010100)
文摘Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study.High resolution has been achieved by Dissipative Compact Schemes(DCS),however,according to the recent research,applications of DCS on complex geometry may have serious problem for that the Geometric Conservation Law(GCL)is not satisfied,and this may cause numerical instability.To cope with this problem,a new scheme named Hybrid cell-edge and cell-node Dissipative Compact Scheme(HDCS)has been formulated.The formulation of the HDCS contains two steps.First,a new central compact scheme is formulated for the purpose of conveniently fulfilling the GCL,and then dissipation is added on the central scheme by high-order dissipative interpolation of cell-edge variables.The solutions of Euler and Navier-Stokes equations show that the HDCS can be applied successfully on complex geometry,while the DCS may suffer numerical instabilities.Moreover,high resolution of the HDCS may be observed in the test of scattering of acoustic waves by multiple cylinders.
