An Entropy-Consistent Flux Scheme for Shallow Water Equations

LIU You-qiong; FENG Jian-hu; LIANG Nan; REN Jiong

doi:10.3879/j.issn.1000-0887.2013.12.003

Volume 34 Issue 12

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LIU You-qiong, FENG Jian-hu, LIANG Nan, REN Jiong. An Entropy-Consistent Flux Scheme for Shallow Water Equations[J]. Applied Mathematics and Mechanics, 2013, 34(12): 1247-1257. doi: 10.3879/j.issn.1000-0887.2013.12.003

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An Entropy-Consistent Flux Scheme for Shallow Water Equations

doi: 10.3879/j.issn.1000-0887.2013.12.003

School of Sciences, Chang’an University, Xi’an 710064, P.R.China

Funds: The National Natural Science Foundation of China（11171043）

Received Date: 2013-05-12
Publish Date: 2013-12-16

Abstract

Abstract

An entropy-consistent flux scheme was developed for the shallow water equations. To offset the entropy increase with cubic order of the shock strength across shock waves, the term of absolute value of the characteristic velocity difference was added into the entropy stable flux, so as to achieve entropy consistency. The new numerical difference scheme featured extreme simplicity, high efficiency, and none additional artificial numerical viscous terms. Numerical experiments of the proposed scheme adequately demonstrated these advantages. The new scheme successfully simulates both the circular shock water wave propagations and the vortices formed on both sides of the breach in different kinds of dam break problems, thus makes a better method to solve the shallow water equations.
- numerical simulation,
- shallow water equations,
- entropy-consistent scheme

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References(13)

References

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