A 3rd-Order Modified Stencil WENO Scheme for Solution of Hyperbolic Conservation Law Equations

WANG Yahui

doi:10.21656/1000-0887.420091

Volume 43 Issue 2

Feb. 2022

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WANG Yahui. A 3rd-Order Modified Stencil WENO Scheme for Solution of Hyperbolic Conservation Law Equations[J]. Applied Mathematics and Mechanics, 2022, 43(2): 224-236. doi: 10.21656/1000-0887.420091

Citation:

WANG Yahui. A 3rd-Order Modified Stencil WENO Scheme for Solution of Hyperbolic Conservation Law Equations[J]. Applied Mathematics and Mechanics, 2022, 43(2): 224-236. doi: 10.21656/1000-0887.420091

Citation:

WANG Yahui. A 3rd-Order Modified Stencil WENO Scheme for Solution of Hyperbolic Conservation Law Equations[J]. Applied Mathematics and Mechanics, 2022, 43(2): 224-236. doi: 10.21656/1000-0887.420091

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A 3rd-Order Modified Stencil WENO Scheme for Solution of Hyperbolic Conservation Law Equations

doi: 10.21656/1000-0887.420091

WANG Yahui

School of Mathematics and Statistics, Zhengzhou Normal University, Zhengzhou 450044, P.R.China

Received Date: 2021-04-10
Accepted Date: 2021-04-10
Rev Recd Date: 2021-09-09

Available Online: 2021-12-27

Publish Date: 2022-02-01

Abstract

Abstract

In order to reduce the numerical dissipation of the classical 3rd-order weighted essentially non-oscillatory (WENO) scheme, a new modified stencil approximation of the 3rd-order WENO scheme was proposed. The 1st-order polynomial approximation of numerical flux on each candidate stencil in the classical WENO-JS3 scheme was improved, and the quadratic term was added to make the stencil approximation reach the 3rd-order accuracy. The corresponding candidate fluxes were calculated. Moreover, the new scheme has essentially non-oscillatory properties through introduction of tunable function φ(x). A series of numerical examples show the effectiveness of the new method.
- hyperbolic conservation law,
- WENO,
- modified stencil,
- nonlinear weight

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References(20)

References

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