Existence of solutions to riemann problem for hyperbolic conservation laws containing δ-shock waves

2001 ◽  
Vol 79 (3-4) ◽  
pp. 419-442
Author(s):  
Ke-pao Lin ◽  
Baolin Sun
Keyword(s):  
Shock Waves ◽  
Conservation Laws ◽  
Riemann Problem ◽  
Hyperbolic Conservation Laws ◽  
Existence Of Solutions ◽  
Hyperbolic Conservation

scholarly journals Symmetries of conservation laws

2005 ◽  
Vol 77 (91) ◽  
pp. 29-51
Author(s):  
Sanja Konjik
Keyword(s):  
Shock Waves ◽  
Conservation Laws ◽  
Gas Dynamics ◽  
Hyperbolic Conservation Laws ◽  
Strong Association ◽  
Group Analysis ◽  
Symmetry Groups ◽  
Dynamics Model ◽  
Hyperbolic Conservation ◽  
Systems Of Conservation Laws

We apply techniques of symmetry group analysis in solving two systems of conservation laws: a model of two strictly hyperbolic conservation laws and a zero pressure gas dynamics model, which both have no global solution, but whose solution consists of singular shock waves. We show that these shock waves are solutions in the sense of 1-strong association. Also, we compute all project able symmetry groups and show that they are 1-strongly associated, hence transform existing solutions in the sense of 1-strong association into other solutions.

Riemann problem for a class of 2 × 2 hyperbolic conservation laws

1996 ◽  
Vol 126 (4) ◽  
pp. 719-724 ◽  
Author(s):  
Changjiang Zhu
Keyword(s):  
Global Existence ◽  
Conservation Laws ◽  
Riemann Problem ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Conservation

In this paper we prove the global existence of the solutions of the Riemann problem for a class of 2 × 2 hyperbolic conservation laws, which is neither necessarily strictly hyperbolic nor necessarily genuinely nonlinear.

A weighted average flux method for hyperbolic conservation laws

1989 ◽  
Vol 423 (1865) ◽  
pp. 401-418 ◽  
Keyword(s):  
Nonlinear Systems ◽  
Conservation Laws ◽  
Riemann Problem ◽  
Model Equation ◽  
Hyperbolic Conservation Laws ◽  
Weighted Average ◽  
Second Order ◽  
Order Accuracy ◽  
Hyperbolic Conservation ◽  
Average Flux

A numerical technique, called a ‘weighted average flux’ (WAF) method, for the solution of initial-value problems for hyperbolic conservation laws is presented. The intercell fluxes are defined by a weighted average through the complete structure of the solution of the relevant Riemann problem. The aim in this definition is the achievement of higher accuracy without the need for solving ‘generalized’ Riemann problems or adding an anti-diffusive term to a given first-order upwind method. Second-order accuracy is proved for a model equation in one space dimension; for nonlinear systems second-order accuracy is supported by numerical evidence. An oscillation-free formulation of the method is easily constructed for a model equation. Applications of the modified technique to scalar equations and nonlinear systems gives results of a quality comparable with those obtained by existing good high resolution methods. An advantage of the present method is its simplicity. It also has the potential for efficiency, because it is well suited to the use of approximations in the solution of the associated Riemann problem. Application of WAF to multidimensional problems is illustrated by the treatment using dimensional splitting of a simple model problem in two dimensions.

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