A modified fifth-order WENO scheme for hyperbolic conservation laws
arXiv:1609.07625 · doi:10.1016/j.camwa.2017.11.020
Abstract
This paper deals with a new fifth-order weighted essentially non-oscillatory (WENO) scheme improving the WENO-NS and WENO-P methods which are introduced in Ha et al. J. Comput. Phys. (2013) and Kim et al., J. Sci. Comput. (2016) respectively. These two schemes provide the fifth-order accuracy at the critical points where the first derivatives vanish but the second derivatives are non-zero. In this paper, we have presented a scheme by defining a new global-smoothness indicator which shows an improved behavior over the solution to the WENO-NS and WENO-P schemes and the proposed scheme attains optimal approximation order, even at the critical points where the first and second derivatives vanish but the third derivatives are non-zero.
arXiv comment23 pages, 14 figures
References in corpus (1)
Cited by in corpus (5)
- Enhancement of shock-capturing methods via machine learning
- Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws
- A general improvement in the WENO-Z-type schemes
- An extension of the order-preserving mapping to the WENO-Z-type schemes
- Construction and comparative study of Euler method with adaptive IQ and IMQ-RBFs