Upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2D

1998 ◽  
Vol 81 (1) ◽  
pp. 85-123 ◽  
Author(s):  
Christian Rohde
Keyword(s):  
Conservation Laws ◽  
Finite Volume ◽  
Hyperbolic Systems ◽  
Finite Volume Schemes ◽  
Weakly Coupled ◽  
Systems Of Conservation Laws

scholarly journals Convergence of finite volume schemes for triangular systems of conservation laws

2008 ◽  
Vol 111 (4) ◽  
pp. 559-589 ◽  
Author(s):  
Kenneth Hvistendahl Karlsen ◽  
Siddhartha Mishra ◽  
Nils Henrik Risebro
Keyword(s):  
Conservation Laws ◽  
Finite Volume ◽  
Finite Volume Schemes ◽  
Triangular Systems ◽  
Systems Of Conservation Laws

On the arithmetic intensity of high-order finite-volume discretizations for hyperbolic systems of conservation laws

2017 ◽  
Vol 33 (1) ◽  
pp. 25-52 ◽  
Author(s):  
J Loffeld ◽  
JAF Hittinger
Keyword(s):  
Conservation Laws ◽  
Finite Volume ◽  
Hyperbolic Systems ◽  
Finite Volume Methods ◽  
High Order ◽  
Floating Point ◽  
Systems Of Conservation Laws ◽  
Data Transfers ◽  
Blue Gene ◽  
Theory And Experiments

It has been conjectured that higher-order discretizations for partial differential equations will have advantages over the lower-order counterparts commonly used today. The reasoning is that the increase in arithmetic operations will be more than offset by the reduction in data transfers and the increase in concurrent floating-point units. To evaluate this conjecture, the arithmetic intensity of a class of high-order finite-volume discretizations for hyperbolic systems of conservation laws is theoretically analyzed for spatial discretizations from orders three through eight in arbitrary dimensions. Three cache models are considered: the limiting cases of no cache and infinite cache as well as a finite-sized cache model. Models are validated experimentally by measuring floating-point operations and data transfers on an IBM Blue Gene/Q node. Theory and experiments demonstrate that high-order finite-volume methods will be able to provide increases in arithmetic intensity that will be necessary to make better utilization of on-node floating-point capability.

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
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