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

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

Mathematics and Computers in Simulation (MATCOM), 2014, vol. 99, issue C, 153-169

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.

Keywords: Shallow water; Implicit time advancing; Defect correction; Exner equation; Morphodynamic flows; Finite-volume schemes (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:99:y:2014:i:c:p:153-169

DOI: 10.1016/j.matcom.2013.07.002

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