High-Order Central Schemes for Hyperbolic Systems of Conservation Laws

1999 ◽  
Vol 21 (1) ◽  
pp. 294-322 ◽  
Author(s):  
Franca Bianco ◽  
Gabriella Puppo ◽  
Giovanni Russo
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Systems ◽  
High Order ◽  
Central Schemes ◽  
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 Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Andrew N. Guarendi ◽  
Abhilash J. Chandy
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Equations ◽  
Hyperbolic Systems ◽  
Scaling Analysis ◽  
Hyperbolic Conservation ◽  
Central Schemes ◽  
Systems Of Conservation Laws ◽  
Ideal Magnetohydrodynamic ◽  
Three Space

We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. Parallel scaling analysis and grid-independent results including contours and isosurfaces of density and velocity and magnetic field vectors are shown in this study, confirming the ability of these types of solvers to approximate the solutions of hyperbolic equations efficiently and accurately.

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