An Improved rd-Order WENO Scheme Based on Mapping Functions and Its Application

XU Wei-zheng; KONG Xiang-shao; WU Wei-guo

doi:10.21656/1000-0887.370345

Volume 38 Issue 10

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Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(10): 1120-1135

XU Wei-zheng, KONG Xiang-shao, WU Wei-guo. An Improved rd-Order WENO Scheme Based on Mapping Functions and Its Application[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1120-1135. doi: 10.21656/1000-0887.370345

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An Improved rd-Order WENO Scheme Based on Mapping Functions and Its Application

doi: 10.21656/1000-0887.370345

¹Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology, Wuhan 430063, P.R.China;²Departments of Naval Architecture, Ocean and Structural Engineering, School of Transportation, Wuhan University of Technology, Wuhan 430063, P.R.China

Funds: The National Natural Science Foundation of China(51409202)

Received Date: 2016-11-14
Rev Recd Date: 2016-12-26
Publish Date: 2017-10-15

Abstract

Abstract

Low-dissipation and high-resolution shock-capturing schemes are of great significance for numerical simulation of flow fields containing shock waves. The WENO-M3 and WENO-MZ3 schemes were proposed with mapping functions based on the classical 3rd-order WENO scheme (WENO-JS3) and the 3rd-order WENO-Z scheme (WENO-Z3). Several classical 1D Riemann problems and double Mach reflection cases were simulated with the above schemes. The simulation results indicate that the WENO-MZ3 scheme has better characteristics of low numerical dissipation and high resolution for the flow features among all the schemes. To expand the application scope of the WENO-MZ3 scheme, the propagation and evolution of blast waves generated by cylindrical high pressure gas in a closed square cabin were investigated. Moreover, 2 typical pressure gauging points on the walls were monitored during the simulation. It is indicated that the WENO-MZ3 scheme is suitable for simulating the evolution of blast waves containing high pressure ratios and high density ratios. The WENO-MZ3 scheme gives lower-dissipation results than the WENO-JS3 scheme for the pressure load on the walls.
- 3rd-order WENO scheme,
- mapping function,
- high resolution,
- low dissipation,
- explosion

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References(19)

References

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