Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must ad...Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.展开更多
In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obt...In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.展开更多
This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves itu uniqueness. A new method of solution constructing is applied, which ...This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves itu uniqueness. A new method of solution constructing is applied, which is different from the usual self-similar transformation. The author also discusses some generalized concepts in multi-dimensional situation (such as 'convex condition', 'left value' and 'right value', etc). An example is finally given to demonstrate that rarefaction wave solution of (1.1)(1.2) is not self-similar.展开更多
The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as th...The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as the condition of solvability is obtained when the solution is required to be of finite order at infinity.展开更多
In this article, Riemann boundary value problem with different factors for polyanalytic functions on the real axis is studied. The expression of solution and sufficient and necessary condition for solvability of the n...In this article, Riemann boundary value problem with different factors for polyanalytic functions on the real axis is studied. The expression of solution and sufficient and necessary condition for solvability of the non-homogeneous Riemann boundary value problem are obtained.展开更多
The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for t...The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for the casep=q=2.展开更多
Solution of the Riemann boundary value problem with square roots(1.1)for analytic functions proposed in[1]is reconsidered,which was solved under certain assumptions on the branch points appeared.Here the work is conti...Solution of the Riemann boundary value problem with square roots(1.1)for analytic functions proposed in[1]is reconsidered,which was solved under certain assumptions on the branch points appeared.Here the work is continued without these assumptions and the problem is solved in the general case.展开更多
By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation ...By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc.展开更多
In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four s...In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.展开更多
In this paper,we study the R m（m〉0） Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C（Vn,n）.By using Plemelj formula,...In this paper,we study the R m（m〉0） Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C（Vn,n）.By using Plemelj formula,we get the solutions of R m（m〉0） Riemann boundary value problems for regular functions.Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions,we obtain the solutions of R m（m〉0） Riemann boundary value problems for harmonic functions and bi-harmonic functions.展开更多
In this article, the authors discuss the Riemann boundary value problems with given principal part. First, authors consider a special case and give a classification of the solution class Rn by the way. And then, they ...In this article, the authors discuss the Riemann boundary value problems with given principal part. First, authors consider a special case and give a classification of the solution class Rn by the way. And then, they consider the general case. The solvable conditions for this problem and its solutions is obtained when it is solvable.展开更多
In this paper, a class of quasi linear Riemann Hilbert problems for general holomorphic functions in the unit disk was studied. Under suitable hypotheses, the existence of solutions of the Hardy class H 2 to this p...In this paper, a class of quasi linear Riemann Hilbert problems for general holomorphic functions in the unit disk was studied. Under suitable hypotheses, the existence of solutions of the Hardy class H 2 to this problem was proved by means of Tikhonov's fixed point theorem and corresponding theories for general holomorphic functions.展开更多
By using the generalized characteristic analysis method, the two-dimensional four-wave Riemann problem for scalar conservation laws, which is nonconvex along the y direction, was studied. Riemann solutions, which invo...By using the generalized characteristic analysis method, the two-dimensional four-wave Riemann problem for scalar conservation laws, which is nonconvex along the y direction, was studied. Riemann solutions, which involve the Guckenheimer structure, were constructed.展开更多
General solution for homogeneous Riemann problems of higher degree is considered.By introducing the concept of loop as well as cross-point,the problem is solved in detail for the quadratic case.The cubic and the quart...General solution for homogeneous Riemann problems of higher degree is considered.By introducing the concept of loop as well as cross-point,the problem is solved in detail for the quadratic case.The cubic and the quartic ones are also analysed.展开更多
Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions hav...Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.展开更多
In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term ...In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.展开更多
The Riemann problem for the chromatography equations in a conservative form is considered. The global solution is obtained under the assumptions that the initial data are taken to be three piecewise constant states. T...The Riemann problem for the chromatography equations in a conservative form is considered. The global solution is obtained under the assumptions that the initial data are taken to be three piecewise constant states. The wave interaction problems are discussed in detail during the process of constructing global solutions to the perturbed Riemann problem. In addition, it can be observed that the Riemann solutions are stable under small perturbations of the Riemann initial data.展开更多
In this paper,the Riemann problem of a Chapman-Jouguet combustion model for the pressure-gradient equations is considered.By analyzing in phase space,existence and uniqueness of the solution to the Riemann problem are...In this paper,the Riemann problem of a Chapman-Jouguet combustion model for the pressure-gradient equations is considered.By analyzing in phase space,existence and uniqueness of the solution to the Riemann problem are obtained constructively under the global entropy conditions.展开更多
Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional （2D） multi-fluid flows, as well as ...Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional （2D） multi-fluid flows, as well as construct the continuous Roe matrix for the whole flow field. The interface capture equations and fluid dynamic conservative equations are coupled together and solved by using any high-resolution schemes that usually suit for the single-fluid flows. Some numerical examples are given to illustrate the solution of 1D and 2D multi-fluid Riemann problems.展开更多
The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin t 0 in the （x, t） plane is considered. Under the modified entropy conditions, the unique solutions are constructed, which ar...The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin t 0 in the （x, t） plane is considered. Under the modified entropy conditions, the unique solutions are constructed, which are the limits of the selfsimilar Zeldovich-von Neumann-Dring （ZND） combustion model. The results show that, for some cases, there are intrinsical differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions. Especially, a strong detonation in the corresponding Riemann solution may be transformed into a weak deflagration coalescing with the pre-compression shock wave after perturbation. Moreover, in some cases, although no combustion wave exists in the corresponding Riemann solution, the combustion wave may occur after perturbation, which shows the instability of the unburnt gases.展开更多
基金Project supported by the National Natural Science Foundation of China(No.12525202)。
文摘Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.
基金supported by National Natural Science Foundation of China (10871199)
文摘In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.
基金National Tian-Yuan Mathematics Foundation of China!Grant No: 1937015
文摘This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves itu uniqueness. A new method of solution constructing is applied, which is different from the usual self-similar transformation. The author also discusses some generalized concepts in multi-dimensional situation (such as 'convex condition', 'left value' and 'right value', etc). An example is finally given to demonstrate that rarefaction wave solution of (1.1)(1.2) is not self-similar.
基金Supported by the National Natural Science Foundation of China !(No.19871064)
文摘The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as the condition of solvability is obtained when the solution is required to be of finite order at infinity.
基金Project supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University.
文摘In this article, Riemann boundary value problem with different factors for polyanalytic functions on the real axis is studied. The expression of solution and sufficient and necessary condition for solvability of the non-homogeneous Riemann boundary value problem are obtained.
文摘The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for the casep=q=2.
文摘Solution of the Riemann boundary value problem with square roots(1.1)for analytic functions proposed in[1]is reconsidered,which was solved under certain assumptions on the branch points appeared.Here the work is continued without these assumptions and the problem is solved in the general case.
基金supported by Natural Science Foundation of China (10071016)the Natural Science Foundation of Fujian Province (2008J0187)the Science and Technology Foundation of Education Department of Fujian Province (JA08255), China
文摘By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc.
基金supported by 973 Key program and the Key Program from Beijing Educational Commission with No. KZ200910028002Program for New Century Excellent Talents in University (NCET)+4 种基金Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR-IHLB)The research of Sheng partially supported by NSFC (10671120)Shanghai Leading Academic Discipline Project: J50101The research of Zhang partially supported by NSFC (10671120)The research of Zheng partially supported by NSF-DMS-0603859
文摘In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.
基金Supported by NSF of China (11171260)RFDP of Higher Eduction of China (20100141110054)
文摘In this paper,we study the R m（m〉0） Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C（Vn,n）.By using Plemelj formula,we get the solutions of R m（m〉0） Riemann boundary value problems for regular functions.Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions,we obtain the solutions of R m（m〉0） Riemann boundary value problems for harmonic functions and bi-harmonic functions.
基金Sponsored by the National NSFC under grant No10471107the Research Foundation for Outstanding Young Teachers, China University of Geosciences(Wuhan)
文摘In this article, the authors discuss the Riemann boundary value problems with given principal part. First, authors consider a special case and give a classification of the solution class Rn by the way. And then, they consider the general case. The solvable conditions for this problem and its solutions is obtained when it is solvable.
文摘In this paper, a class of quasi linear Riemann Hilbert problems for general holomorphic functions in the unit disk was studied. Under suitable hypotheses, the existence of solutions of the Hardy class H 2 to this problem was proved by means of Tikhonov's fixed point theorem and corresponding theories for general holomorphic functions.
文摘By using the generalized characteristic analysis method, the two-dimensional four-wave Riemann problem for scalar conservation laws, which is nonconvex along the y direction, was studied. Riemann solutions, which involve the Guckenheimer structure, were constructed.
基金Supported by the Science Foundation of NSC,P.R.China
文摘General solution for homogeneous Riemann problems of higher degree is considered.By introducing the concept of loop as well as cross-point,the problem is solved in detail for the quadratic case.The cubic and the quartic ones are also analysed.
文摘Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.
文摘In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.
基金Supported by NSFC(11371240 and 11771274)the grant of "The First-Class Discipline of Universities in Shanghai"
文摘The Riemann problem for the chromatography equations in a conservative form is considered. The global solution is obtained under the assumptions that the initial data are taken to be three piecewise constant states. The wave interaction problems are discussed in detail during the process of constructing global solutions to the perturbed Riemann problem. In addition, it can be observed that the Riemann solutions are stable under small perturbations of the Riemann initial data.
基金Project supported by the National Natural Science Foundation of China (Grant No.10971130)and the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘In this paper,the Riemann problem of a Chapman-Jouguet combustion model for the pressure-gradient equations is considered.By analyzing in phase space,existence and uniqueness of the solution to the Riemann problem are obtained constructively under the global entropy conditions.
文摘Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional （2D） multi-fluid flows, as well as construct the continuous Roe matrix for the whole flow field. The interface capture equations and fluid dynamic conservative equations are coupled together and solved by using any high-resolution schemes that usually suit for the single-fluid flows. Some numerical examples are given to illustrate the solution of 1D and 2D multi-fluid Riemann problems.
基金Project supported by the National Natural Science Foundation of China(No.10971130)the Shanghai Leading Academic Discipline Project(No.J50101)+1 种基金the Shanghai Municipal Education Commission of Scientific Research Innovation Project(No.11ZZ84)the Graduate Innovation Foundation of Shanghai University
文摘The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin t 0 in the （x, t） plane is considered. Under the modified entropy conditions, the unique solutions are constructed, which are the limits of the selfsimilar Zeldovich-von Neumann-Dring （ZND） combustion model. The results show that, for some cases, there are intrinsical differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions. Especially, a strong detonation in the corresponding Riemann solution may be transformed into a weak deflagration coalescing with the pre-compression shock wave after perturbation. Moreover, in some cases, although no combustion wave exists in the corresponding Riemann solution, the combustion wave may occur after perturbation, which shows the instability of the unburnt gases.
