A fourth-order central Runge-Kutta scheme for hyperbolic conservation laws

2009 ◽  
Vol 26 (6) ◽  
pp. 1675-1692 ◽  
Author(s):  
Mehdi Dehghan ◽  
Rooholah Jazlanian
Keyword(s):  
Conservation Laws ◽  
Fourth Order ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Conservation ◽  
Runge Kutta

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.

New optimized implicit-explicit Runge-Kutta methods with applications to the hyperbolic conservation laws

2021 ◽  
pp. 110650
Author(s):  
Praveen K. Maurya ◽  
Vivek S. Yadav ◽  
Bikash Mahato ◽  
Naveen Ganta ◽  
Manoj K. Rajpoot ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Conservation ◽  
Runge Kutta
Sign in / Sign up

Export Citation Format

Share Document