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Thursday, October 8, 2020 | History

3 edition of two-dimensional Riemann problem in gas dynamics found in the catalog.

two-dimensional Riemann problem in gas dynamics

Jiequan Li

two-dimensional Riemann problem in gas dynamics

by Jiequan Li

  • 248 Want to read
  • 2 Currently reading

Published by Longman in Harlow .
Written in English

    Subjects:
  • Conservation laws (Mathematics),
  • Finite differences.,
  • Gas dynamics -- Mathematics.,
  • Lagrange equations -- Numerical solutions.,
  • Riemann-Hilbert problems.

  • Edition Notes

    Includes bibliographical references and index.

    StatementJiequan Li, Tong Zhang and Shuli Yang.
    SeriesPitman monographs and surveys in pure and applied mathematics -- 98
    ContributionsYang, Shuli., Zhang, Tong, 1932-
    Classifications
    LC ClassificationsQA930 .L5 1998
    The Physical Object
    Paginationx, 300 p. :
    Number of Pages300
    ID Numbers
    Open LibraryOL22250200M
    ISBN 100582244080

      Two-dimensional Riemann problem for Chaplygin gas dynamics in four pieces Journal of Mathematical Analysis and Applications, Vol. , No. 1 Using potential flow theory and conformal mapping technique to measure pressure differential on airfoil. The initial-value problem constructed by Riemann () to describe the motion of an ideal gas in a shock tube is investigated analytically, with an emphasis on the mathematical aspects. Topics addressed include the simplest Riemann model and the interactions of elementary waves (shock waves, centered rarefaction waves, and contact discontinuities), one-dimensional isothermal flow, one.

    In addition, one can also see [7,8,15] for the Riemann problem on the relativistic version of Chaplygin gas equations and [5, 6,13,24,31,40] for the Riemann problem on the two-dimensional.   In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which have been merely discussed so : Wancheng Sheng.

    A. Kurganov and E. Tadmor, Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numer. Methods Partial Differential Equations, 18 (), doi: /num Google Scholar [19]. Abstract. This paper is a survey of some recent development on the zero-pressure gas dynamics. We will state the mechanism of delta-shock and its propagation, construct the solutions of one-dimensional and two-dimensional Riemann problems, and then prove the existence of solutions to the general Cauchy problem.


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Two-dimensional Riemann problem in gas dynamics by Jiequan Li Download PDF EPUB FB2

The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics, clarifies the boundaries of interaction of elementary waves, demonstrates the interesting spatial interaction of slip lines, and proposes a series of open problems.

The Riemann problem for two-dimensional flow of polytropic gas with three constant initial data is considered. Under the assumption that each interface of initial data outside of the origin projects exactly one planar wave of shock, rar.

The Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or two-dimensional Riemann problem in gas dynamics book line connects two neighboring constant initial by: We report here on our numerical study of the two-dimensional Riemann problem for the compressible Euler equations.

Compared with the relatively simple 1-D configurations, the 2-D case consists of a. imate the solution of the two-dimensional Riemann problem for gas dynamics, using the literal extension of the well-known HLL formalism as its basis.

Essentially, any strategy attempting to extend the three-state HLL Riemann solver to multiple space dimensions will by some means in. In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively.

In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which havea been merely discussed so far. In Riemann problems for two-dimensional gas dynamics the initial data are con- stant in each quadrant, so restricted that only one elementary wave, a one-dimensional shock, a one-dimensional rarefaction, or a two-dimensional slip line (a contact discon- tinuity) appears at each interface.

InZhang and Zheng conjectured on the structure of a solution for a four quadrant Riemann problem for two-dimensional (2−D) gas dynamics system: (1){ρt+(ρu)x+(ρv)y=0,(ρu)t+(ρu2+p)x+(ρuv)y=0,(ρv)t+(ρuv)x+(ρv2+p)y=0,for the isentropic flow p=Aργ,γ>1,A>0,and for the adiabatic flow.

Euler Equations of Gas Dynamics called invariants,3 are transported along particular curves in the plane (x,t), called a numerical point of view, this suggests a simple way to calculate the solution in any point P(x,t) by gathering all the in- formation transported through the characteristics starting from P and going back to regions where the solution is already.

We solve a two-d Riemann problem over the computational domain, with initial conditions given by and Dirichlet boundary conditions (i.e., the conserved quantities take on the values specified by the initial conditions at either boundary).

The solution is evolved up. The Two-Dimensional Riemann Problem in Gas Dynamics (Monographs and Surveys in Pure and Applied Mathematics) by Li, Jiequan, Yang, Shuli, Zhang, Tong. and a great selection of related books, art and collectibles available now at Two-dimensional flow of polytropic gas with initial data being constant in each quadrant is considered.

Under the assumption that each jump in initial data outside of the origin projects exactly one planar wave of shocks, centered rarefaction waves, or slip planes, it Cited by: This text deals with the two-dimensional Riemann problem for Euler equations in gas dynamics and its mathematical simplification.

For Euler equations it is classified into 18 cases according to the different combinations of four elementary plane waves emanated by initial discontinuities. Two-dimensional Riemann problems arise when one-dimensional waves cross or overtake one another or when these waves reflect from or interact with walls or boundaries.

Generally, an interaction will arise when two waves meet or a single wave meets a boundary; it is such simple and generic problems which are fundamental. Wang, B. Chen, and Y.

Hu, “The two-dimensional Riemann problem for Chaplygin gas dynamics with three constant states,” Journal of Mathematical Analysis & Applications, vol.pp. –, The Riemann problems for two-dimensional zero-pressure gas dynamics are solved completely when the initial data take three constant states having discontinuities on x,y-positive and x-negative axes.

With the help of characteristic analysis, by studying. We are concerned with the Riemann problem for the two-dimensional compressible Euler equations in gas dynamics.

The central point at this issue is the dynamical interaction of shock waves, centered rarefaction waves, and contact discontinuities that connect two neighboring constant initial states in the quadrants.

The Riemann problem is classified into eighteen genuinely different cases. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We report here on our numerical study of the two-dimensional Riemann problem for the compressible Euler equations.

Compared with the relatively simple 1-D configurations, the 2-D case consists of a plethora of geometric wave patterns which pose a computational challenge for highresolution methods. The solution of the Riemann problem for this simple linear system consists of two jumps, one proportional to each of the eigenvectors of $A$, and each moving with.

Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers. By Alexander Kurganov and Eitan Tadmor. Cite. BibTex; Full citation; Publisher: Wiley.

Year: DOI identifier: /num OAI identifier: Provided by: MUCC (Crossref). In these fields, Riemann problems are calculated using Riemann solvers. The Riemann problem in linearized gas dynamics.

As a simple example, we investigate the properties of the one-dimensional Riemann problem in gas dynamics (Toro, Eleuterio F. (). Riemann Solvers and Numerical Methods for Fluid Dynamics, Pg 44, Example ).The positivity principle and positive schemes to solve multidimensional hyperbolic systems of conservation laws have been introduced in [X.-D.

Liu and P. D. Lax, J. Fluid Dynam., 5 (), pp. ].Some numerical experiments presented there show how well the method works.Kurganov A., and Tadmor E.: Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numer.

Methods Partial Diff. Eqs. – ().