A Well-Balanced HLL Scheme for Hyperbolic Conservation Systems With Source Terms

PENG Guoliang; WANG Zhongqi; ZHANG Junjie; REN Zeping; XIE Haiyan; DU Taijiao

doi:10.21656/1000-0887.430084

Volume 44 Issue 1

Jan. 2023

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Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(1): 105-111

PENG Guoliang, WANG Zhongqi, ZHANG Junjie, REN Zeping, XIE Haiyan, DU Taijiao. A Well-Balanced HLL Scheme for Hyperbolic Conservation Systems With Source Terms[J]. Applied Mathematics and Mechanics, 2023, 44(1): 105-111. doi: 10.21656/1000-0887.430084

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A Well-Balanced HLL Scheme for Hyperbolic Conservation Systems With Source Terms

doi: 10.21656/1000-0887.430084

1.
School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, P.R.China
2.
Northwest Institute of Nuclear Technology, Xi’an 710024, P.R.China

Received Date: 2022-03-15
Accepted Date: 2022-07-01
Rev Recd Date: 2022-06-09

Available Online: 2022-12-27

Publish Date: 2023-01-01

Abstract

Abstract

A new finite volume scheme was proposed for hyperbolic conservation systems with source terms. The classical finite volume schemes could not accurately simulate the dynamic problems caused by the balance between flux terms and source terms. To deal with this problem, an approximate Riemann solver with source terms was designed in accordance with the classical HLL approximate Riemann solver. The well-balanced HLL scheme (WB-HLL) was obtained through modification of the flux calculation schemes for 1D Euler equations and ideal MHD equations with gravity source terms, and a proof for the well-balanced property of the new scheme was presented. Two numerical examples of 1D Euler equations and ideal MHD equations demonstrate that the proposed WB-HLL scheme has higher accuracy and faster convergence than the classical HLL ones.
- hyperbolic conservation system,
- source term,
- approximate Riemann solver,
- well-balanced HLL scheme,
- finite volume scheme

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References(14)

References

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