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.

scholarly journals Symmetries of conservation laws

2005 ◽  
Vol 77 (91) ◽  
pp. 29-51
Author(s):  
Sanja Konjik
Keyword(s):  
Shock Waves ◽  
Conservation Laws ◽  
Gas Dynamics ◽  
Hyperbolic Conservation Laws ◽  
Strong Association ◽  
Group Analysis ◽  
Symmetry Groups ◽  
Dynamics Model ◽  
Hyperbolic Conservation ◽  
Systems Of Conservation Laws

We apply techniques of symmetry group analysis in solving two systems of conservation laws: a model of two strictly hyperbolic conservation laws and a zero pressure gas dynamics model, which both have no global solution, but whose solution consists of singular shock waves. We show that these shock waves are solutions in the sense of 1-strong association. Also, we compute all project able symmetry groups and show that they are 1-strongly associated, hence transform existing solutions in the sense of 1-strong association into other solutions.

AN EFFICIENT THIRD-ORDER SCHEME FOR THREE-DIMENSIONAL HYPERBOLIC CONSERVATION LAWS

2012 ◽  
Vol 03 (04) ◽  
pp. 1250015
Author(s):  
LI CAI ◽  
JIAN-HU FENG ◽  
YU-FENG NIE ◽  
WEN-XIAN XIE
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Three Dimensional ◽  
Upwind Scheme ◽  
Third Order ◽  
Hyperbolic Conservation ◽  
Weighted Essentially Nonoscillatory ◽  
Order Scheme ◽  
Cweno Reconstruction ◽  
Three Space

In this paper, we present a third-order central weighted essentially nonoscillatory (CWENO) reconstruction for computations of hyperbolic conservation laws in three space dimensions. Simultaneously, as a Godunov-type central scheme, the CWENO-type central-upwind scheme, i.e., the semi-discrete central-upwind scheme based on our third-order CWENO reconstruction, is developed straightforwardly to solve 3D systems by the so-called componentwise and dimensional-by-dimensional technologies. The high resolution, the efficiency and the nonoscillatory property of the scheme can be verified by solving several numerical experiments.

scholarly journals Optimal jump set in hyperbolic conservation laws

2020 ◽  
Vol 17 (04) ◽  
pp. 765-784
Author(s):  
Shyam Sundar Ghoshal ◽  
Animesh Jana
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Entropy Solution ◽  
Hyperbolic Systems ◽  
Scalar Case ◽  
Qualitative Properties ◽  
Hyperbolic Conservation ◽  
Scalar Conservation Law ◽  
Scalar Conservation ◽  
Jump Set

We investigate qualitative properties of entropy solutions to hyperbolic conservation laws, and construct an entropy solution to a scalar conservation law for which the jump set is not closed, in particular, it is dense in a space-time domain. In a second part, we establish a similar result for hyperbolic systems. We give two different approaches for scalar conservation laws and hyperbolic systems in order to obtain these results. For the scalar case, the solutions are explicitly calculated.

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