Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We consider the Saint-Venant system for shallow water flows, with nonflat bottom. It is a hyperbolic system of conservation laws that approximately describes various geophysical flows, such as rivers, coastal areas, and oceans when completed with a Coriolis term, or granular flows when completed with friction. Numerical approximate solutions to this system may be generated using conservative finite volume methods, which are known to properly handle shocks and contact discontinuities. However, in general these schemes are known to be quite inaccurate for near steady states, as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions. This difficulty can be overcome by using the so-called well-balanced schemes. We describe a general strategy, based on a local hydrostatic reconstruction, that allows us to derive a well-balanced scheme from any given numerical flux for the homogeneous problem. Whenever the initial solver satisfies some classical stability properties, it yields a simple and fast well-balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality.

A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows

Mes premiers remtrciements trout aux auteurs des 206 communications th6matiquts et notes de projet, sans qui ces actes n'auraient 6videmment pas vu le jour. / Is oat contribu6 h la qualit6 scientifique et ,5 I'hmuog6t~6it6 pr6sentationntlle de leurs articles en refondant les versions iuitiales soumises an comit6 de programme, ea acceptant de suivre les r~gles de pr6sentation indiqu6es, et en nous envoyant parrots plusieurs versions am61ior6es surun point ou sur l'autrc.

/pdf/about-these-proceedings-4s0qpzq930.pdf

About these proceedings

Numerical resolution of well-balanced shallow water equations with complex source terms

https://hal.inria.fr/inria-00071808/document

A five equation reduced model for compressible two phase flow problems

https://hal.archives-ouvertes.fr/hal-01290889/document

Some approximate Godunov schemes to compute shallow-water equations with topography

We study here a model of conservative nonlinear conservation law with a flux function with discontinuous coefficients, namely the equation ut + (k(x)u(1 - u))x = 0. It is a particular entropy condition on the line of discontinuity of the coefficient k which ensures the uniqueness of the entropy solution. This condition is discussed and justified. On the other hand, we perform a numerical analysis of the problem. Two finite volume schemes, the Godunov scheme and the VFRoe-ncv scheme, are proposed to simulate the conservation law. They are compared with two finite volume methods classically used in an industrial context. Several tests confirm the good behavior of both new schemes, especially through the discontinuity of permeability k (whereas a loss of accuracy may be detected when industrial methods are performed). Moreover, a modified MUSCL method which accounts for stationary states is introduced.

https://hal.archives-ouvertes.fr/hal-01376535/document

Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients

We consider numerical solutions of the two-dimensional non-linear shallow water equations with a bed slope source term. These equations are well-suited for the study of many geophysical phenomena, including coastal engineering where wetting and drying processes are commonly observed. To accurately describe the evolution of moving shorelines over strongly varying topography, we first investigate two well-balanced methods of Godunov-type, relying on the resolution of non-homogeneous Riemann problems. But even if these schemes were previously proved to be efficient in many simulations involving occurrences of dry zones, they fail to compute accurately moving shorelines. From this, we investigate a new model, called SURF_WB, especially designed for the simulation of wave transformations over strongly varying topography. This model relies on a recent reconstruction method for the treatment of the bed-slope source term and is able to handle strong variations of topography and to preserve the steady states at rest. In addition, the use of the recent VFRoe-ncv Riemann solver leads to a robust treatment of wetting and drying phenomena. An adapted ‘second order’ reconstruction generates accurate bore-capturing abilities.This scheme is validated against several analytical solutions, involving varying topography, time dependent moving shorelines and convergences toward steady states. This model should have an impact in the prediction of 2D moving shorelines over strongly irregular topography. Copyright © 2006 John Wiley & Sons, Ltd.

https://www.epoc.u-bordeaux.fr/indiv/bonneton/publications/papers/papers-nearshore/Marche_etal2007.pdf

Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes.

The shallow water model with a source term due to topography gradient is approximated within the frame of Finite Volume numerical methods. The cornerstone of the method is the solution of the inhomogeneous Riemann problem. Thus the numerical scheme can deal simultaneously with discrete steady states, flood, occurrence and covering of dry zones. We present the parameterization through the discontinuity of topography, emphasizing on the resonance phenomenon. We then build the solution of the inhomogeneous Riemann problem using a continuation method with respect to the jump of topography. Finally, numerical experiments illustrate the agreement of the numerical method with the previous analysis.

A well-balanced numerical scheme for the approximation of the shallow-water equations with topography: the resonance phenomenon

https://hal.archives-ouvertes.fr/hal-01484345/document

Nicolas Seguin

Papers

Some approximate Godunov schemes to compute shallow-water equations with topography

Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients

Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes.

A well-balanced numerical scheme for the approximation of the shallow-water equations with topography: the resonance phenomenon

Closure laws for a two-fluid two-pressure model