High resolution numerical schemes for solving kinematic wave equation

Chunshui Yu, Jennifer G. Duan

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


This paper compares the stability, accuracy, and computational cost of several numerical methods for solving the kinematic wave equation. The numerical methods include the second-order MacCormack finite difference scheme, the MacCormack scheme with a dissipative interface, the second-order MUSCL finite volume scheme, and the fifth-order WENO finite volume scheme. These numerical schemes are tested against several synthetic cases and an overland flow experiment, which include shock wave, rarefaction wave, wave steepening, uniform/non-uniform rainfall generated overland flows, and flow over a channel of varying bed slope. The results show that the MacCormack scheme is not a Total Variation Diminishing (TVD) scheme because oscillatory solutions occurred at the presence of shock wave, rarefaction wave, and overland flow over rapidly varying bed slopes. The MacCormack scheme with a dissipative interface is free of oscillation but with considerable diffusions. The Godunov-type schemes are accurate and stable when dealing with discontinuous waves. Furthermore the Godunov-type schemes, like MUSCL and WENO scheme, are needed for simulating surface flow from spatially non-uniformly distributed rainfalls over irregular terrains using moderate computing resources on current personal computers.

Original languageEnglish (US)
Pages (from-to)823-832
Number of pages10
JournalJournal of Hydrology
Issue numberPA
StatePublished - Nov 7 2014


  • Godunov-type scheme
  • Kinematic wave equation
  • MacCormack scheme
  • Rainfall-runoff overland flow
  • Rarefaction wave
  • Shock wave

ASJC Scopus subject areas

  • Water Science and Technology


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