The Riemann problem for the one-dimensional compressible flow of a van der Waals gas

被引：0
作者：
Yicheng Pang
Min Hu
机构：
[1] Guizhou University of Finance and Economics,School of Mathematics and Statistics
来源：
Zeitschrift für angewandte Mathematik und Physik | 2019年 / 70卷
关键词：
System of balance laws; Compressible fluid; Riemann problem; 35L65; 35L67;
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摘要：
We address the Riemann problem for the one-dimensional compressive flow of a van der Waals gas, in which the external force is a given continuous function of time. The explicit forms for shock wave, contact discontinuity and rarefaction wave are presented. The influence of van der Waals parameter on these elementary waves is discussed. Furthermore, we obtain six kinds of solutions to this Riemann problem and establish a condition for the occurrence of vacuum in the solutions. Particularly, all of the solutions are not self-similar in (t, x)-plane due to the presence of the time-dependent external force.
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  • [1] Kraiko AN(1979)Discontinuity surfaces in medium without self-pressure Prikl. Math. Mech. 43 539-549
  • [2] Nedeljkov M(2010)Shadow waves, entropies and interactions for delta and singular shocks Arch. Ration. Mech. Anal. 197 489-537
  • [3] Nilsson B(2011)Mass, momentum and energy conservation laws in zero-pressure gas dynamics and delta-shocks: II Appl. Anal. 90 831-842
  • [4] Rozanova OS(2011)Mass, momentum and energy conservation laws in zero-pressure gas dynamics and delta-shocks Appl. Anal. 90 1677-1689
  • [5] Shelkovich VM(2012)Riemann problem for one-dimensional system of conservation laws of mass, momentum and energy in zero-pressure gas dynamics Differ. Equ. Appl. 4 653-664
  • [6] Nilsson B(1965)Solutions in the large for nonlinear systems of equations Comm. Pure Appl. Math. 18 697-715
  • [7] Shelkovich VM(2010)The Riemann problem of adiabatic Chaplygin gas dynamic system Commun. Appl. Math. Comput. 24 9-16
  • [8] Cheng H(2017)Delta shock wave in the compressible Euler equations for a Chaplygin gas J. Math. Anal. Appl. 448 245-261
  • [9] Glimm J(2016)Delta shock wave with Dirac delta function in multiple components for the system of generalized Chaplygin gas dynamics Bound. Value Probl. 2016 1-20
  • [10] Zhu L(2016)Riemann problem in non-ideal gas dynamics Indian J. Pure Appl. Math. 47 501-521
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