A mass-conservative centered finite volume model for solving two-dimensional two-layer shallow water equations for fluid mud propagation over varying topography and dry areas

Canestrelli, Alberto; Fagherazzi, Sergio; Lanzoni, Stefano

doi:10.1016/j.advwatres.2012.01.009

Cited by 21 publications

(8 citation statements)

References 52 publications

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“…The numerical procedure requires particular attention. Indeed, in order to ensure mass conservation with an acceptable accuracy in the context of long‐term simulations, the numerical scheme must ensure mass conservation and satisfy the so‐called well‐balanced property, whereby a quiescent steady state is reproduced with sufficient accuracy by the numerical algorithm [ Canestrelli et al , , ; Canestrelli and Toro , ].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Where river and tide meet: The morphodynamic equilibrium of alluvial estuaries

Pittaluga

Tambroni

Canestrelli

et al. 2015

J. Geophys. Res. Earth Surf.

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We investigate the morphodynamic equilibrium of tidally dominated alluvial estuaries, extending previous works concerning the purely tidal case and the combined tidal‐fluvial case with a small tidal forcing. We relax the latter assumption and seek the equilibrium bed profile of the estuary, for a given planform configuration with various degrees of funneling, solving numerically the 1‐D governing equation. The results show that with steady fluvial and tidal forcings, an equilibrium bed profile of estuaries exists. In the case of constant width estuaries, a concave down equilibrium profile develops through most of the estuary. Increasing the amplitude of the tidal oscillation, progressively higher bed slopes are experienced at the mouth while the river‐dominated portion of the estuary experiences an increasing bed degradation. The fluvial‐marine transition is identified by a “tidal length” that increases monotonically as the river discharge and the corresponding sediment supply are increased while the river attains a new morphological equilibrium configuration. Tidal length also increases if, for a fixed river discharge and tidal amplitude, the sediment flux is progressively reduced with respect to the transport capacity. In the case of funnel‐shaped estuaries the tidal length strongly decreases, aggradation is triggered by channel widening, and tidal effects are such to enhance the slope at the inlet and the net degradation of the river bed. Finally, results suggest that alluvial estuaries in morphological equilibrium cannot experience any amplification of the tidal wave propagating landward. Hence, hypersynchronous alluvial estuaries cannot be in equilibrium.

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Section: Formulation Of the Problemmentioning

confidence: 99%

Where river and tide meet: The morphodynamic equilibrium of alluvial estuaries

Pittaluga

Tambroni

Canestrelli

et al. 2015

J. Geophys. Res. Earth Surf.

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“…Because of the free‐slip condition at the walls, the 2D problem reduces to a one‐dimensional problem. Its analytical solution was first proposed by Stoker , and it is often used to test the ability of numerical models to deal with discontinuities in the flow field (, among others). For this test case, the advective terms are discretized explicitly in both ADI stages, following the momentum‐conserving approach proposed by Stelling and Duinmeijer , which leads to the following stability constraint:

\frac{normald t u_{max}}{normald x} < 1, \frac{normald t v_{max}}{normald y} < 1

where u max and v max are the maximum velocities achieved in x and y directions, respectively.…”

Section: Resultsmentioning

confidence: 99%

A mass‐conservative staggered immersed boundary model for solving the shallow water equations on complex geometries

Canestrelli

Spruyt

Jagers

et al. 2015

Numerical Methods in Fluids

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SUMMARYIn this work, an approach is proposed for solving the 3D shallow water equations with embedded boundaries that are not aligned with the underlying horizontal Cartesian grid. A hybrid cut-cell/ghost-cell method is used together with a direction-splitting implicit solver: Ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells, and conserves fluid mass up to machine precision. Moreover, the solver displays a second-order spatial accuracy, both globally and locally. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method.

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“…Two-layer shallow-water equations (SWE) are widely used to simulate geophysical flows in stratified conditions. Some examples of a two-layer configuration include exchange flows in sea straits [15,14], highly stratified estuaries [23,24], as well as various types of gravity currents [27,3], such as mudflows [7], debris flows [35,30], submarine avalanches [20,29,36], and pyroclastic flows [19]. Although such processes can be described more accurately by 3D Navier-Stokes equations, two-layer shallow water models make a popular alternative because of their simplicity and a significantly lower computational cost.…”

Section: Introductionmentioning

confidence: 99%

Re-evaluating efficiency of first-order numerical schemes for two-layer shallow water systems by considering different eigenvalue solutions

Krvavica

2020

Advances in Water Resources

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The efficiency of several first-order numerical schemes for two-layer shallow water equations (SWE) are evaluated here by considering different eigenvalue solutions. This study is a continuation of our previous work [25] in which we have proposed an efficient implementation of a Roe solver for two-layer SWE based on analytical expressions for eigenvalues and eigenvectors. In this work, the accuracy and computational cost of numerical, analytical, and approximated eigenvalue solvers are compared when implemented in Roe, Intermediate Field CaPturing (IFCP) and Polynomial Viscosity Matrix (PVM) schemes. Several

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A mass-conservative centered finite volume model for solving two-dimensional two-layer shallow water equations for fluid mud propagation over varying topography and dry areas

Cited by 21 publications

References 52 publications

Where river and tide meet: The morphodynamic equilibrium of alluvial estuaries

Where river and tide meet: The morphodynamic equilibrium of alluvial estuaries

A mass‐conservative staggered immersed boundary model for solving the shallow water equations on complex geometries

Re-evaluating efficiency of first-order numerical schemes for two-layer shallow water systems by considering different eigenvalue solutions

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