Higher order accuracy finite-difference schemes for hyperbolic conservation laws

1982 ◽  
Vol 18 (7) ◽  
pp. 1019-1029 ◽  
Author(s):  
A. Sivasankara Reddy
Keyword(s):  
Finite Difference ◽  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Higher Order ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Order Accuracy ◽  
Hyperbolic Conservation

scholarly journals A Fourth Order Entropy Stable Scheme for Hyperbolic Conservation Laws

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 508 ◽  
Author(s):  
Xiaohan Cheng
Keyword(s):  
Conservation Laws ◽  
Fourth Order ◽  
Hyperbolic Conservation Laws ◽  
Order Accuracy ◽  
Hyperbolic Conservation ◽  
Diffusion Operator ◽  
Sign Property ◽  
Entropy Stable ◽  
Order Four ◽  
Stable Scheme

This paper develops a fourth order entropy stable scheme to approximate the entropy solution of one-dimensional hyperbolic conservation laws. The scheme is constructed by employing a high order entropy conservative flux of order four in conjunction with a suitable numerical diffusion operator that based on a fourth order non-oscillatory reconstruction which satisfies the sign property. The constructed scheme possesses two features: (1) it achieves fourth order accuracy in the smooth area while keeping high resolution with sharp discontinuity transitions in the nonsmooth area; (2) it is entropy stable. Some typical numerical experiments are performed to illustrate the capability of the new entropy stable scheme.

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