A shallow water type model to describe the dynamic of thin partially wetting films for the simulation of anti-icing systems

2018 ◽  
Author(s):  
Julien Lallement ◽  
Pierre Trontin ◽  
Claire Laurent ◽  
Philippe Villedieu
Keyword(s):  
Shallow Water ◽  
Type Model ◽  
Water Type ◽  
Wetting Films

scholarly journals Multilayer shallow-water model with stratification and shear

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 351
Author(s):  
F. J. Beron-Vera
Keyword(s):  
Shallow Water ◽  
Baroclinic Instability ◽  
Single Layer ◽  
Vertical Shear ◽  
Water Model ◽  
Type Model ◽  
Inhomogeneous Layer ◽  
Good Representation ◽  
Water Type ◽  
Dissipation Energy

The purpose of this paper is to present a shallow-water-type model with multiple inhomogeneous layers featuring variable linear velocity vertical shear and startificaion in horizontal space and time. This is achieved by writing the layer velocity and buoyancy fields as linear functions of depth, with coefficients that depend arbitrarily on horizontal position and time. The model is a generalization of Ripa's (1995) single-layer model to an arbitrary number of layers. Unlike models with homogeneous layers the present model is able to represent thermodynamics processes driven by heat and freshwater fluxes through the surface or mixing processes resulting from fluid exchanges across contiguous layers. By contrast with inhomogeneous-layer models with depth-independent velocity and buoyancy, the model derived here can sustain explicitly at low frequency a current in thermal wind balance (between the vertical vertical shear and the horizontal density gradient) within each layer. In the absence of external forcing and dissipation, energy, volume, mass, and buoyancy variance constrain the dynamics; conservation of total zonal momentum requires in addition the usual zonal symmetry of the topography and horizontal domain.  The inviscid, unforced model admits a formulation suggestive of a generalized Hamiltonian structure, which enables the classical connection between symmetries and conservation laws via Noether's theorem.  A steady solution to a system involving one Ripa-like layer and otherwise homogeneous layers can be proved formally (or Arnold) stable using the above invariants. A model configuration with only one layer has been shown previously to provide: a very good representation of the exact vertical normal modes up to the first internal mode; an exact representation of long-perturbation (free boundary) baroclinic instability; and a very reasonable representation of short-perturbation (classical Eady) baroclinic instability. Here it is shown that substantially more accurate overall results with respect to single-layer calculations can be achieved by considering a stack of only a few layers. A similar behavior is found in ageostrophic (classical Stone) baroclinic instability by describing accurately the dependence of the solutions on the Richardson number with only two layers.

A two-layer shallow flow model with two axes of integration with application to submarine avalanches and generated tsunamis

2021 ◽  
Author(s):  
Enrique D. Fernandez-Nieto ◽  
François Bouchut ◽  
Juan M. Delgado-Sanchez ◽  
Anne Mangeney ◽  
Gladys Narbona-Reina
Keyword(s):  
Shallow Water ◽  
Granular Layer ◽  
Water Layer ◽  
Type Model ◽  
Water Type ◽  
Time Step ◽  
Cartesian Coordinates ◽  
Local Coordinates ◽  
Averaged Model ◽  
Granular Surface

<p>There exits in the literature many approaches that has been used to model submarine avalanches (See [5]). These models are mainly based on the pioneer work of Savage and Hutter (SH) [4] that is a shallow water type model for aerial avalanches, which is written in local coordinates, in order to simulate the tangential velocity to the bottom. A depth-averaged SH model over a general bottom with curvature was introduced in [1]. An extension to submarine avalanches is developed in [2]. In this paper the same local coordinate system is used for the two layers. Nevertheless, using a local coordinates the model would prescribe the perturbation at the surface at a wrong placement. In [3] a bilayer depth-averaged model for submarine avalanches is presented with cartesian coordinates for the water layer and local coordinates for the avalanche. The drawback is that the seabed deformation is considered as an input data for the water layer equations, then no interaction between the two fluids are taken into account and it is necessary to do an interpolation of the granular surface at each time step of the numerical simulation. In this work we present firstly the details of the proposed model, a coupled two-layer shallow water system where we consider local coordinates for the granular layer and cartesian coordinates for the fluid one. The main difference with other models that adopt the same stragie is that any interpolation of the granular surface is required. Moreover, the velocity of the granular layer has an explicit influence on the mass and momentum conservation laws of the fluid layer. Secondly, several numerical tests will be presented.</p><p>References</p><p>[1] F. Bouchut, E.D. Fernández-Nieto, A. Mangeney, and P.Y. Lagrée. On new erosion models of Savage-Hutter type for avalanches. Acta Mechanica, 199(1):181--208, 2008.<br>[2] E.D. Fernández-Nieto, F. Bouchut, D. Bresch, M.J. Castro Díaz, and A. Mangeney. A new Savage-Hutter type model for submarine avalanches and generated tsunami. Journal of Computational Physics, 227(16):7720--7754, 2008.<br>[3] P.H. Heinrich, A. Piatanesi, and H. Hébert. Numerical modelling of tsunami generation and propagation from submarine slumps: the 1998 papua new guinea event. Geophysical Journal International, 145(1):97--111, 2001.<br>[4] S. B. Savage and K. Hutter. The dynamics of avalanches of granular materials from initiation to runout. part I: Analysis. Acta Mechanica, 86(1):201–223, 1991.<br>[5] S. Yavari-Ramshe and B. Ataie-Ashtiani. Numerical modeling of subaerial and submarine landslide-generated tsunami waves-recent advances and future challenges. Landslides, 13(6):1325–1368, 2016.</p>

scholarly journals The Lituya Bay landslide-generated mega-tsunami. Numerical simulation and sensitivity analysis

2018 ◽  
Author(s):  
José Manuel González-Vida ◽  
Jorge Macías ◽  
Manuel Jesús Castro ◽  
Carlos Sánchez-Linares ◽  
Marc de la Asunción ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Sensitivity Analysis ◽  
Numerical Model ◽  
Shallow Water ◽  
Extreme Event ◽  
Fluid Model ◽  
Model Parameters ◽  
Water Type ◽  
Bathymetric Data ◽  
Run Up

Abstract. The 1958 Lituya Bay landslide-generated mega-tsunami is simulated using the Landslide-HySEA model, a recently developed finite volume Savage-Hutter Shallow Water coupled numerical model. Two factors are crucial if the main objective of the numerical simulation is to reproduce the maximal run-up, with an accurate simulation of the inundated area and a precise re-creation of the known trimline of the 1958 mega-tsunami of Lituya Bay. First, the accurate reconstruction of the initial slide. Then, the choice of a suitable coupled landslide-fluid model able to reproduce how the energy released by the landslide is transmitted to the water and then propagated. Given the numerical model, the choice of parameters appears to be a point of major importance, this leads us to perform a sensitivity analysis. Based on public domain topo-bathymetric data, and on information extracted from the work of Miller (1960), an approximation of Gilbert Inlet topo-bathymetry was set up and used for the numerical simulation of the mega-event. Once optimal model parameters were set, comparisons with observational data were performed in order to validate the numerical results. In the present work, we demonstrate that a shallow water type of model is able to accurately reproduce such an extreme event as the Lituya Bay mega-tsunami. The resulting numerical simulation is one of the first successful attempts (if not the first) at numerically reproducing in detail the main features of this event in a realistic 3D basin geometry, where no smoothing or other stabilizing factors in the bathymetric data are applied.

scholarly journals Water ow on vegetated hill. 1D shallow water equation type model

2015 ◽  
Vol 23 (3) ◽  
pp. 83-96 ◽  
Author(s):  
Stelian Ion ◽  
Dorin Marinescu ◽  
Anca Veronica Ion ◽  
Stefan Gicu Cruceanu ◽  
Virgil Iordache
Keyword(s):  
Mathematical Model ◽  
Shallow Water ◽  
Numerical Approximation ◽  
Approximation Scheme ◽  
Shallow Water Equation ◽  
Simplified Model ◽  
Type Model ◽  
Curvature Radius ◽  
Geometrical Properties ◽  
Mathematical Properties

Abstract A mathematical model for the water ow on a hill covered by variable distributed vegetation is proposed in this article. The model takes into account the variation of the geometrical properties of the terrain surface, but it assumes that the surface exhibits large curvature radius. After describing some theoretical properties for this model, we introduce a simplified model and a well-balanced numerical approximation scheme for it. Some mathematical properties with physical relevance are discussed and finally, some numerical results are presented.

scholarly journals Weak Local Residuals as Smoothness Indicators in Adaptive Mesh Methods for Shallow Water Flows

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 345
Author(s):  
Sudi Mungkasi ◽  
Stephen Gwyn Roberts
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Adaptive Mesh ◽  
Finite Volume Methods ◽  
Water Type ◽  
Two Dimensional ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Smoothness Indicators

This paper proposes some formulations of weak local residuals of shallow-water-type equations, namely, one-, one-and-a-half-, and two-dimensional shallow water equations. Smooth parts of numerical solutions have small absolute values of weak local residuals. Rougher parts of numerical solutions have larger absolute values of weak local residuals. This behaviour enables the weak local residuals to detect parts of numerical solutions which are smooth and rough (non-smooth). Weak local residuals that we formulate are implemented successfully as refinement or coarsening indicators for adaptive mesh finite volume methods used to solve shallow water equations.

Stability of the Camassa-Holm peakons in the dynamics of a shallow-water-type system

2016 ◽  
Vol 55 (2) ◽  
Author(s):  
Robin Ming Chen ◽  
Xiaochuan Liu ◽  
Yue Liu ◽  
Changzheng Qu
Keyword(s):  
Shallow Water ◽  
Type System ◽  
Water Type

Sponges and the Chalk Rock

1962 ◽  
Vol 99 (3) ◽  
pp. 273-278 ◽  
Author(s):  
R. E. H. Reid
Keyword(s):  
Shallow Water ◽  
Deep Water ◽  
Water Type ◽  
Direct Bearing ◽  
Water Conditions ◽  
Rock Lithology

AbstractChalk Rock lithology suggests shallow-water conditions, but the fauna has been said (Woods, 1897; Jukes-Brown, 1904) to imply a depth between about 100–500 fm. A study of the sponges which are numerous in the Oxfordshire–Hertfordshire area shows that these form a fauna of the sort which is typical of the Chalk as a whole, with Hexactinellida predominant as was pointed out by Woods; this is a fauna of deep-water type by both modern and Cretaceous standards. The depth which these sponges imply need, however, not be much more than 100 fm., and their presence need have no direct bearing on the depth at which erosional features were formed.

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