A high order staggered grid method for hyperbolic systems of conservation laws in one space dimension

1989 ◽  
Vol 75 (1-3) ◽  
pp. 91-107 ◽  
Author(s):  
Richard Sanders ◽  
Alan Weiser
Keyword(s):  
Conservation Laws ◽  
Space Dimension ◽  
Hyperbolic Systems ◽  
Grid Method ◽  
High Order ◽  
Staggered Grid ◽  
Systems Of Conservation Laws ◽  
One Space Dimension

scholarly journals On hyperbolic systems with entropy velocity covariant under the action of a group

2015 ◽  
Vol 12 (04) ◽  
pp. 763-785
Author(s):  
François Dubois
Keyword(s):  
Conservation Laws ◽  
Space Dimension ◽  
Hyperbolic Systems ◽  
Sufficient Conditions ◽  
Space Time ◽  
Systems Of Conservation Laws ◽  
Time Transformations ◽  
One Space Dimension

For hyperbolic systems of conservation laws in one space dimension endowed with a mathematical entropy, we define the notion of entropy velocity and we give sufficient conditions for such a system to be covariant under the action of a group of space-time transformations. These conditions naturally introduce a representation of the group in the space of states. We construct such hyperbolic systems from the knowledge of data on the manifold of null velocity. We apply these ideas for Galileo, Lorentz, and circular groups and, in particular, focus on nontrivial examples of [Formula: see text] 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.

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