Delta shock wave as self-similar viscosity limit for a strictly hyperbolic system of conservation laws

2019 ◽  
Vol 60 (5) ◽  
pp. 051510 ◽  
Author(s):  
Anupam Sen ◽  
T. Raja Sekhar
Keyword(s):  
Shock Wave ◽  
Conservation Laws ◽  
Hyperbolic System ◽  
Delta Shock Wave ◽  
Delta Shock ◽  
System Of Conservation Laws ◽  
Viscosity Limit ◽  
Self Similar

scholarly journals Delta shock wave for a 3 × 3 hyperbolic system of conservation laws

2016 ◽  
Vol 47 (1) ◽  
pp. 277-290
Author(s):  
Richard De la cruz ◽  
Juan Galvis ◽  
Juan Carlos Juajibioy ◽  
Leonardo Rendón
Keyword(s):  
Shock Wave ◽  
Conservation Laws ◽  
Hyperbolic System ◽  
Delta Shock Wave ◽  
Delta Shock ◽  
System Of Conservation Laws

scholarly journals Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Hongjun Cheng
Keyword(s):  
Shock Waves ◽  
Conservation Laws ◽  
Hyperbolic System ◽  
Delta Shock Wave ◽  
Riemann Solutions ◽  
Delta Shock ◽  
System Of Conservation Laws ◽  
Elementary Waves ◽  
Delta Shock Waves ◽  
Linearly Degenerate

This paper is devoted to the study of delta shock waves for a hyperbolic system of conservation laws of Keyfitz-Kranzer type with two linearly degenerate characteristics. The Riemann problem is solved constructively. The Riemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solution are established. These analytical results match well the numerical ones. Finally, two kinds of interactions of elementary waves are discussed.

scholarly journals On a Nonsymmetric Keyfitz-Kranzer System of Conservation Laws with Generalized and Modified Chaplygin Gas Pressure Law

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Hongjun Cheng ◽  
Hanchun Yang
Keyword(s):  
Shock Wave ◽  
Conservation Laws ◽  
Chaplygin Gas ◽  
Gas Pressure ◽  
Modified Chaplygin Gas ◽  
Delta Shock Wave ◽  
Generalized Chaplygin Gas ◽  
Riemann Solutions ◽  
Delta Shock ◽  
System Of Conservation Laws

This paper is devoted to the study of a nonsymmetric Keyfitz-Kranzer system of conservation laws with the generalized and modified Chaplygin gas pressure law, which may admit delta shock waves, a topic of interest. Firstly, we solve the Riemann problems with piecewise constant data having a single discontinuity. For the generalized Chaplygin gas pressure law, the solution consists of three different structures:R+J,S+J, andδ. Existence and uniqueness of delta shock solution are established under the generalized Rankine-Hugoniot relation and entropy condition. For the modified Chaplygin gas pressure law, the structures of solution areR+JandS+J. Secondly, we discuss the limits of Riemann solutions for the modified Chaplygin gas pressure law as the pressure law tends to the generalized Chaplygin gas one. In particular, for some cases, the solutionS+Jtends to a delta shock wave, and it is different from the delta shock wave for the generalized Chaplygin gas pressure law with the same initial data. Thirdly, we simulate the Riemann solutions and examine the formation process of delta shock wave by employing the Nessyahu-Tadmor scheme. The numerical results are coincident with the theoretical analysis.

Delta Shock Wave in a Perfect Fluid Model with Zero Pressure

2019 ◽  
Vol 74 (9) ◽  
pp. 767-775 ◽  
Author(s):  
Yicheng Pang ◽  
Jianjun Ge ◽  
Min Hu ◽  
Liuyang Shao
Keyword(s):  
Shock Wave ◽  
Continuous Function ◽  
Perfect Fluid ◽  
External Force ◽  
Fluid Model ◽  
Delta Function ◽  
Delta Shock Wave ◽  
Dirac Delta ◽  
Delta Shock ◽  
Self Similar

AbstractThe Riemann problem for a perfect fluid model with zero pressure is considered, where the external force is a given continuous function of time. All of exact solutions are given. In particular, a vacuum occurs in the solutions, although initial data stay far away from the vacuum. It is shown that a delta shock wave in which density and internal energy contain a Dirac delta function develops in the solutions. The position, velocity, and weights of the delta shock wave are presented explicitly. Moreover, all of the solutions are not self-similar because of the presence of the external force.

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