Journal of Scientific Computing

, Volume 79, Issue 2, pp 891–913 | Cite as

High Order Residual Distribution for Steady State Problems for Hyperbolic Conservation Laws

  • Jianfang Lin
  • Rémi AbgrallEmail author
  • Jianxian Qiu


In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used to compute the numerical fluxes and source term based on the point values of the solution, and the principles of residual distribution schemes are adapted to obtain steady state solutions. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency, high order accuracy and the capability of resolving shocks of the proposed methods.


Residual distribution WENO-ZQ integration High order accuracy Conservation laws 



J. Lin and J. Qiu are partly supported by NSFC Grant 11571290 and NSAF Grant U1630247, J. Lin also is supported by the China Scholarship Council and SNF Grant FZEB-0-166980. This work was performed while the first author was visiting the Institute of Mathematics, University of Zurich.


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Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Institute of MathematicsUniversity of ZurichZurichSwitzerland
  3. 3.School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamenPeople’s Republic of China

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