Two-dimensional Riemann problem for a hyperbolic system of conservation laws in three pieces

Pang, Yicheng; Tian, Jianjun Paul; Yang, Hanchun

doi:10.1016/j.amc.2012.08.010

Cited by 6 publications

(3 citation statements)

References 41 publications

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“…With these types of initial data, many important components of the two-dimensional Riemann problems can be determined for various systems of conservation laws (see [1,2,11,15,16] and the references therein). In the present study, we are concerned with the two-dimensional Riemann problem for system (1.1) where (s i , c i ) = (0, 0), i = 1, 2, 3, are different constant values, and (μ 0 , ν 0 ) is a given unit normal vector of the corresponding initial discontinuity.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional Riemann problem involving three contact discontinuities for 2×2 hyperbolic conservation laws in anisotropic media

Pang

Yang

2015

Journal of Mathematical Analysis and Applications

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In this study, we consider the two-dimensional Riemann problem for a system of conservation laws, which models polymer flooding in an anisotropic oil reservoir. The initial data are constants in three sectors centered at the origin, which only involve three contact discontinuities. By the generalized characteristic analysis method and the phase plane analysis method, we find that the solutions are not unique for certain values of the initial data. We propose an additional stability condition for the interaction of the contact discontinuities. By this stability condition, all of the exact solutions and their corresponding criteria can be obtained. The solutions exhibit various geometrical structures. In particular, envelope rarefaction waves develop in some solutions.

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Section: Introductionmentioning

confidence: 99%

Two-dimensional Riemann problem involving three contact discontinuities for 2×2 hyperbolic conservation laws in anisotropic media

Pang

Yang

2015

Journal of Mathematical Analysis and Applications

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“…They found the delta shock in this model independently of Korchinski, and Tan et al [5] established the concept of a delta shock. In addition, Pang et al [6,7], and Shen [8] considered three constant initial data for the system (3).…”

Section: Introductionmentioning

confidence: 99%

Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock

Hwang¹,

Shin²,

Shin³

et al. 2021

Mathematics

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In this paper, a four-quadrant Riemann problem for a 2×2 system of hyperbolic conservation laws is considered in the case of delta shock appearing at the initial discontinuity. We also remove the restriction in that there is only one planar wave at each initial discontinuity. We include the existence of two elementary waves at each initial discontinuity and classify 14 topologically distinct solutions. For each case, we construct an analytic solution and compute the numerical solution.

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“…By this method, many excellent achievements are developed for the others two-dimensional systems of conservation laws. See [1,2,[8][9][10][11][12] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Non-selfsimilar global solutions to a two-dimensional system of conservation laws

Pang

Wang

Zhao³

2017

Math. Meth. Appl. Sci.

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Communicated by S. ChenThis paper considers the two-dimensional Riemann problem for a system of conservation laws that models the polymer flooding in an oil reservoir. The initial data are two different constant states separated by a smooth curve. By virtue of a nonlinear coordinate transformation, this problem is converted into another simple one. We then analyze rigorously the expressions of elementary waves. Based on these preparations, we obtain respectively four kinds of non-selfsimilar global solutions and their corresponding criteria. It is shown that the intermediate state between two elementary waves is no longer a constant state and that the expression of the rarefaction wave is obtained by constructing an inverse function. These are distinctive features of the non-selfsimilar global solutions.

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Two-dimensional Riemann problem for a hyperbolic system of conservation laws in three pieces

Cited by 6 publications

References 41 publications

Two-dimensional Riemann problem involving three contact discontinuities for 2×2 hyperbolic conservation laws in anisotropic media

Two-dimensional Riemann problem involving three contact discontinuities for 2×2 hyperbolic conservation laws in anisotropic media

Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock

Non-selfsimilar global solutions to a two-dimensional system of conservation laws

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