A fast finite volume solver for multi-layered shallow water flows with mass exchange

Abstract

(2014) 'A fast nite volume solver for multi-layered shallow water ows with mass exchange.', Journal of computational physics., 272 . pp. 23-45. Further information on publisher's website:http://dx.doi.org/10.1016/j.jcp.2014.04.026Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Journal of Computational Physics, 272, 2014Physics, 272, , 10.1016Physics, 272, /j.jcp.2014 Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractA fast finite volume solver for hydrostatic multi-layered shallow water flows with mass exchange is investigated. In contrast to many models for multi-layered hydrostatic shallow water flows where the immiscible suppression is assumed, the present model allows for mass exchange between the layers. The multi-layered shallow water equations form a system of conservation laws with source terms for which the computation of the eigenvalues is not trivial. For most practical applications, complex eigenvalues may arise in the system and the multi-layered shallow water equations are not hyperbolic any more. This property makes the application of conventional finite volume methods difficult or even impossible for those methods which require in their formulation the explicit computation of the eigenvalues. In the current study, we propose a finite volume method that avoids the solution of Riemann problems. At each time step, the method consists of two stages to update the new solution. In the first stage, the multilayered shallow water equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed from the intermediate solutions in the first stage and used in the conservative form of the multi-layered shallow water equations. The proposed method is simple to implement, satisfies the conservation property and is suitable for multi-layered shallow water equations on non-flat topography. The proposed finite volume solver is verified against several benchmark tests and it shows good agreement with analytical solutions of the incompressible hydrostat...

2D granular flows with the μ(I) rheology and side walls friction: A well-balanced multilayer discretization

“…In the literature, multilayer systems have been discretized by combining a usual finite volume method with a splitting procedure [1,2,4,5,6,21]. Thus, authors usually separate the viscous terms, which are treated with a semi-implicit scheme.…”

New Numerical Algorithm for the Multi-Layer Shallow Water Equations Based on the Hyperbolic Decomposition and the CABARET Scheme

“…The computational grid rearrangement and the resulting exchange of mass and momentum between the layers largely regularize the problem [15,[32][33][34], however, in this case the proper choice of filtrering parameters and artificial viscosity remains very important. The calculation was carried out according to the CABARET scheme according to a single-layer model and at 10 N = number of layers on the sigma-coordinate with the same layer thicknesses up to 6 t = point in time corresponding to more than one period of surface oscillation.…”

“…Another approach to the solution of this problem is to modify the classical equations of multilayer shallow water -to remove the prohibition of mass and momentum exchange between layers [14,15]. In fact, this means a transition from the Lagrangian description of the vertical motion of the layer boundaries to the mixed Euler-Lagrangian description [16].…”

New Numerical Algorithm for the Multi-Layer Shallow Water Equations Based on the Hyperbolic Decomposition and the CABARET Scheme

“…Другой подход к решению указанной проблемы заключается в модификации классических уравнений многослойной мелкой воды -снятии запрета обмена массой и импульсом между слоями [14,15]. Фактически это означает переход от лагранжевого описания вертикального движения границ слоев к смешанному эйлеро-лагранжевому описанию [16].…”