scholarly journals Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term

2019 ◽  
Vol 18 (3) ◽  
pp. 1523-1545 ◽  
Author(s):  
Yu Zhang ◽  
◽  
Yanyan Zhang ◽  
Keyword(s):  
Conservation Laws ◽  
Source Term ◽  
Hyperbolic Systems ◽  
Riemann Problems ◽  
Systems Of Conservation Laws

scholarly journals Numerical solutions of hyperbolic systems of conservation laws combining unsteady friction and viscoelastic pipes

2020 ◽  
Author(s):  
Aboudou Seck
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Finite Volume ◽  
Source Term ◽  
Numerical Solutions ◽  
Pipe Wall ◽  
Hyperbolic Systems ◽  
Mass Conservation ◽  
Viscoelastic Effects ◽  
Systems Of Conservation Laws

Abstract The main contribution of the paper is to incorporate pipe-wall viscoelastic and unsteady friction in the derivation of the water-hammer solutions of non-conservative hyperbolic systems with conserved quantities as variables. The system is solved using the Godunov finite volume scheme to obtain numerical solutions. This results in the appearance of a new term in the mass conservation equation of the classical governing system. This new numerical algorithm implements the Godunov approach to one-dimensional hyperbolic systems of conservation laws on a finite volume stencil. The viscoelastic pipe-wall response in the mass conservation part of the source term has been modeled using generalized Kelvin–Voigt theory. For the momentum part of the source term a fast, robust and accurate numerical scheme linked to the Lambert W-function for calculating the friction factor has been used. A case study has been used to illustrate the influence of the various formulations; a comparison between the classical solution, the numerical solution including quasi-steady friction, the numerical solution incorporating the viscoelastic effects, and measurements are presented. The inclusion of viscoelastic effects results in better agreement between the measured and solved values.

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
Sign in / Sign up

Export Citation Format

Share Document