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
Citation: 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

An Entropy-Consistent Flux Scheme for Shallow Water Equations

doi: 10.3879/j.issn.1000-0887.2013.12.003
Funds:  The National Natural Science Foundation of China(11171043)
  • Received Date: 2013-05-12
  • Publish Date: 2013-12-16
  • 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.
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