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Implicit time advancing combined with two finite-volume methods in the simulation of morphodynamic flows

Author

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  • Bilanceri, M.
  • Beux, F.
  • Elmahi, I.
  • Guillard, H.
  • Salvetti, M.V.

Abstract

Numerical simulation of morphodynamic problems is considered. The physical model is based on the shallow-water equations coupled with the Exner equation closed by the Grass model to describe the time evolution of the bed profile. The SRNH predictor–corrector scheme and a modified Roe scheme for non-conservative systems of equations are considered for space discretization. Second-order accuracy in space is achieved through variable reconstruction. These schemes were previously used in the simulation of the considered problems together with explicit time advancing. Linearized implicit time-advancing versions are generated here, in which the flux Jacobians are computed through automatic differentiation. Second-order accuracy in time is obtained through a backward differentiation formula associated with a defect-correction approach. For both the considered numerical methods, the explicit and implicit versions are compared in terms of accuracy and efficiency for one-dimensional and two-dimensional morphodynamic problems characterized by different time scales for the evolution of the bed and of the water flow.

Suggested Citation

  • Bilanceri, M. & Beux, F. & Elmahi, I. & Guillard, H. & Salvetti, M.V., 2014. "Implicit time advancing combined with two finite-volume methods in the simulation of morphodynamic flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 153-169.
    • Handle: RePEc:eee:matcom:v:99:y:2014:i:c:p:153-169
    DOI: 10.1016/j.matcom.2013.07.002
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    References listed on IDEAS

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    1. Benkhaldoun, Fayssal & Daoudi, Salah & Elmahi, Imad & Seaïd, Mohammed, 2011. "Comparison of unstructured finite-volume morphodynamic models in contracting channel flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2087-2097.
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