# Shallow Water Equations

### 2 Discrete formulation of the shallow water equations

**equations**are derived from depth-integrating the Navier-Stokes

**equations**in the case where the horizontal length scale is much greater than the vertical length ...derivation

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### Modified method of characteristics for the shallow water equations

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**equations**; Open channel Flow, Numerical models; Method of Characteristics 1 - Introduction Flow in open channels is frequently modelled using a staggered finite difference ...

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### Symmetry Properties and Solutions of Shallow Water Equations

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### A Fast and Compact Solver for the Shallow Water Equations

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**equations**. The

**water**velocity and height variables are collocated on a uniform grid and a novel, unified scheme is used to advect all quantities ...

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### Efficient solvers for the shallow water equations on a sphere

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**equations**on a sphere involving satellite data. We ...

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### Imperfect bifurcation for the quasi geostrophic shallow water equations

**Shallow**-

**Water**...Euler

**equations**, likely separates into an infinite set of disjoint branches for any finite value of the Rossby deformation length ε −1 ...

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### A Similarity Technique for Solving Two Layer Shallow Water Equations

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**equations**representing gravity ...

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### Comparison of variational balance models for the rotating shallow water equations

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**equations**over a moderate interval of time chosen such that the Eulerian fields experience an order one relative ...full

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### FLOODING AND DRYING IN DISCONTINUOUS GALERKIN DISCRETIZATIONS OF SHALLOW WATER EQUATIONS

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### Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations

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**Equations**[5, 6, 7] has been ...classic

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**Equations**on a Representative Elementary Volume containing the fluid phase and the obstacles [5, ...

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### A unified surface-gradient and hydrostatic reconstruction scheme for the shallow water equations

**water**depth and depth-averaged horizontal velocities and g is the gravitational ...the

**equations**is in divergence form and governs conservation of mass and momentum, and the right hand side is a ...

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### Well-balanced computations of weak local residuals for the shallow water equations

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**equations**describe mass con- servation and momentum conservation. We propose a well-balanced numerical ...

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### Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations

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**equations**. In order to address well-balancing and positivity-preserving we have added some ...

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### Modelling rapid mass movements using the shallow water equations in Cartesian coordinates

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**equations**and in the general formulation of Bouchut and Westdickenberg (2004), the acceleration due to gravity being the driving force depends on the gradient of the fluid surface, ...

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### A study of well-balanced finite volume methods and refinement indicators for the shallow water equations

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**equations**analytically and nu- merically. The study is separated into three parts. The first part is about well-balanced finite volume ...

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### CiteSeerX — ON THE PHYSICAL RELEVANCE OF THE DAM BREAK PROBLEM IN THE CONTEXT OF NONLINEAR SHALLOW WATER EQUATIONS

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**equations**...Nonlinear

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**Equations**(NSWE) are widely used for flood- ing ...total

**water**depth ...

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### On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

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**equations**. J. Comp. Phys., 225, 1233-1261. 4. Anderson Jr., J. D., 1995: ...

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### Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography

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### A novel entropy stable discontinuous Galerkin spectral element method for the shallow water equations on GPUs

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**equations**, we proceed to address the general two dimensional ...form

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**equations**with metric term splitting include many distinct terms, ...

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### New Numerical Algorithm for the Multi-Layer Shallow Water Equations Based on the Hyperbolic Decomposition and the CABARET Scheme

**equations**system for each ...hyperbolic

**equations**with variable density in each ...multilayer

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**equations**is not unconditionally hyperbolic, and in case hyperbolicity is ...

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