A general approximate-state Riemann solver for hyperbolic systems of conservation laws with source terms

2007 ◽  
Vol 53 (9) ◽  
pp. 1509-1540 ◽  
Author(s):  
Julien Lhomme ◽  
Vincent Guinot
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Riemann Solver ◽  
Source Terms ◽  
Systems Of Conservation Laws

scholarly journals A Hybrid Riemann Solver for Large Hyperbolic Systems of Conservation Laws

2017 ◽  
Vol 39 (6) ◽  
pp. A2911-A2934 ◽  
Author(s):  
Birte Schmidtmann ◽  
Manuel Torrilhon
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Riemann Solver ◽  
Systems Of Conservation Laws

A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS

2001 ◽  
Vol 11 (02) ◽  
pp. 339-365 ◽  
Author(s):  
LAURENT GOSSE
Keyword(s):  
Asymptotic Behavior ◽  
Conservation Laws ◽  
Euler Equations ◽  
Hyperbolic Systems ◽  
Zero Order ◽  
Inhomogeneous System ◽  
Source Terms ◽  
First Order ◽  
Systems Of Conservation Laws ◽  
The Right

The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a non-conservative reformulation of the zero-order terms of the right-hand side of the equations. In this context, we decided to use the results of Dal Maso, Le Floch and Murat about non-conservative products, and the generalized Roe matrices introduced by Toumi to derive a first-order linearized well-balanced scheme in the sense of Greenberg and Le Roux. As a main feature, this approach is able to preserve the right asymptotic behavior of the original inhomogeneous system, which is not an obvious property. Numerical results for the Euler equations are shown to handle correctly these equilibria in various situations.

scholarly journals On the uniqueness of solutions to hyperbolic systems of conservation laws

2021 ◽  
Vol 291 ◽  
pp. 110-153
Author(s):  
Shyam Sundar Ghoshal ◽  
Animesh Jana ◽  
Konstantinos Koumatos
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
Uniqueness Of Solutions ◽  
Systems Of Conservation Laws
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