A 1D shallow-flow model for two-layer flows based on FORCE scheme with wet–dry treatment

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 cons...

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Bibliographic Details
Published in:Journal of hydroinformatics 2020-09, Vol.22 (5), p.1015-1037
Main Authors: Martínez-Aranda, S., Ramos-Pérez, A., García-Navarro, P.
Format: Article
Language:English
Subjects:
Accuracy
Coexistence
Computational fluid dynamics
Conservation
Conservation laws
Conservation of momentum
Eigenvalues
Flow velocity
Fluids
Friction
Lakes
Mathematical models
Model accuracy
Model testing
Momentum
One dimensional models
Partial differential equations
Robustness (mathematics)
Shear stress
Steady flow
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Summary: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.
ISSN:1464-7141
1465-1734
DOI:10.2166/hydro.2020.002