The reconstruction of upwind fluxes for conservation laws, its behavior in dynamic and steady state calculations

Hwajeong Choi Temple University Jian-Guo Liu Temple University

Numerical Analysis and Scientific Computing mathscidoc:1702.25063

Journal of Computational Physics, 144, (2), 237–256, 1998.8
The Euler equation of compressible flows is solved by the finite volume method, where high order accuracy is achieved by the reconstruction of each component of upwind fluxes of a flux splitting using the biased averaging procedure. Compared to the solution reconstruction in Godunov-type methods, its implementation is simple and easy, and the computational complexity is relatively low. This approach is parameter-free and requires neither a Riemann solver nor field-by-field decomposition. The numerical results from both dynamic and steady state calculations demonstrate the accuracy and robustness of this approach. Some techniques for the acceleration of the convergence to the steady state are discussed, including multigrid and multistage Runge–Kutta time methods.
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@inproceedings{hwajeong1998the,
  title={The reconstruction of upwind fluxes for conservation laws, its behavior in dynamic and steady state calculations},
  author={Hwajeong Choi, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209125341671498395},
  booktitle={Journal of Computational Physics},
  volume={144},
  number={2},
  pages={237–256},
  year={1998},
}
Hwajeong Choi, and Jian-Guo Liu. The reconstruction of upwind fluxes for conservation laws, its behavior in dynamic and steady state calculations. 1998. Vol. 144. In Journal of Computational Physics. pp.237–256. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209125341671498395.
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