Affiliation:
1. Fluid Mechanics, University of Zaragoza, Zaragoza, Spain
Abstract
Abstract
The two-layer problem is defined as the coexistence of two immiscible fluids, separated by an interface surface. Under the shallow-flow hypothesis, 1D models are based on a four equations system accounting for the mass and momentum conservation in each fluid layer. Mathematically, the system of conservation laws modelling 1D two-layer flows has the important drawback of loss of hyperbolicity, causing that numerical schemes based on the eigenvalues of the Jacobian become unstable. In this work, well-balanced FORCE scheme is proposed for 1D two-layer shallow flows. The FORCE scheme combines the first-order Lax–Friedrichs flux and the second-order Lax–Wendroff flux. The scheme is supplemented with a hydrostatic reconstruction procedure in order to ensure the well-balanced behaviour of the model for steady flows even under wet–dry conditions. Additionally, a method to obtain high-accuracy numerical solutions for two-layer steady flows including friction dissipation is proposed to design reference benchmark tests for model validation. The enhanced FORCE scheme is faced to lake-at-rest benchmarking tests and steady flow cases including friction, demonstrating its well-balanced character. Furthermore, the numerical results obtained for highly unsteady two-layer dambreaks are used to analyse the robustness and accuracy of the model under a wide range of flow conditions.
Funder
Ministerio de Ciencia, Innovación y Universidades
Fundación General CSIC
Subject
Atmospheric Science,Geotechnical Engineering and Engineering Geology,Civil and Structural Engineering,Water Science and Technology
Reference31 articles.
1. Two-layer shallow water system: a relaxation approach;SIAM Journal of Scientific Computing,2010
2. One-dimensional two-fluid equations for horizontal stratified two-phase flow;International Journal of Multiphase Flow,1980
3. The hydraulics of two flowing layers with different densities;Journal of Fluid Mechanics,1986
4. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows;Siam Journal on Scientific Computing,2004
5. Lower Mississippi salinity analysis;Journal of Hydraulic Engineering,1985
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