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

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.
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https://hal.inria.fr/hal-00871717
Contributor : Herve Guillard <>
Submitted on : Thursday, October 10, 2013 - 11:36:09 AM
Last modification on : Tuesday, February 26, 2019 - 10:55:14 AM

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Marco Bilanceri, Francois Beux, Imad Elmahi, Hervé Guillard, Maria Vittoria Salvetti. Implicit time advancing combined with two finite-volume methods in the simulation of morphodynamic flows. Mathematics and Computers in Simulation, Elsevier, 2014, 99, pp.153-169. ⟨10.1016/j.matcom.2013.07.002⟩. ⟨hal-00871717⟩

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