Volume 12, Issue 4
A Fourth Order WENO Scheme for Hyperbolic Conservation Laws

Xiaohan Cheng, Jianhu Feng & Supei Zheng

Adv. Appl. Math. Mech., 12 (2020), pp. 992-1007.

Published online: 2020-06

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  • Abstract

In this work, a fourth order weighted essentially non-oscillatory (WENO) scheme is developed for hyperbolic conservation laws. The new reconstruction is a convex combination of three linear reconstructions. To keep high order accuracy in smooth regions and maintain non-oscillatory near discontinuities, the nonlinear weights are carefully designed. The main advantage of the proposed scheme is that the scheme achieves one order of improvement in accuracy in smooth regions compared with the classical third order scheme when using the same spatial nodes. Several benchmark examples are presented to verify the scheme's fourth order accuracy and capacity of dealing with problems containing complicated structures.

  • Keywords

Hyperbolic conservation laws, WENO scheme, nonlinear weights, Euler equations.

  • AMS Subject Headings

65M06, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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