scholarly journals A finite volume shock-capturing solver of the fully coupled shallow water-sediment equations

2017 ◽  
Vol 84 (9) ◽  
pp. 509-542 ◽  
Author(s):  
Maggie J. Creed ◽  
Ilektra-Georgia Apostolidou ◽  
Paul H. Taylor ◽  
Alistair G.L. Borthwick
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shock Capturing ◽  
Fully Coupled ◽  
Shallow Water Sediment

scholarly journals LAGRANGIAN DRIFTER MODELLING OF AN EXPERIMENTAL RIP CURRENT

2012 ◽  
Vol 1 (33) ◽  
pp. 35
Author(s):  
Leandro Suarez ◽  
Rodrigo Cienfuegos ◽  
Eric Barthélemy ◽  
Hervé Michallet ◽  
Cristian Escauriaza
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Hydrodynamic Model ◽  
Shallow Water Equations ◽  
Shock Capturing ◽  
Rip Current ◽  
Wave Forcing ◽  
Nearshore Circulation ◽  
Mean Circulation ◽  
Lagrangian Drifter

A non-uniform alongshore wave forcing on an experimental uneven mobile bathymetry create mean circulation on a rip channel. A 2D numerical hydrodynamic model that integrates the non-linear shallow-water equations in a shock-capturing finite-volume framework is used to validate the nearshore circulation, and drifters displacement.

scholarly journals A Finite-Volume Icosahedral Shallow-Water Model on a Local Coordinate

2009 ◽  
Vol 137 (4) ◽  
pp. 1422-1437 ◽  
Author(s):  
Jin-Luen Lee ◽  
Alexander E. MacDonald
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Spherical Surface ◽  
Second Order ◽  
Water Model ◽  
Numerical Dissipation ◽  
Shallow Water Model ◽  
Finite Volume Model ◽  
Volume Model ◽  
Cartesian Coordinate

Abstract An icosahedral-hexagonal shallow-water model (SWM) on the sphere is formulated on a local Cartesian coordinate based on the general stereographic projection plane. It is discretized with the third-order Adam–Bashforth time-differencing scheme and the second-order finite-volume operators for spatial derivative terms. The finite-volume operators are applied to the model variables defined on the nonstaggered grid with the edge variables interpolated using polynomial interpolation. The projected local coordinate reduces the solution space from the three-dimensional, curved, spherical surface to the two-dimensional plane and thus reduces the number of complete sets of basis functions in the Vandermonde matrix, which is the essential component of the interpolation. The use of a local Cartesian coordinate also greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. The SWM is evaluated with the standard test cases of Williamson et al. Numerical results show that the icosahedral SWM is free from Pole problems. The SWM is a second-order finite-volume model as shown by the truncation error convergence test. The lee-wave numerical solutions are compared and found to be very similar to the solutions shown in other SWMs. The SWM is stably integrated for several weeks without numerical dissipation using the wavenumber 4 Rossby–Haurwitz solution as an initial condition. It is also shown that the icosahedral SWM achieves mass conservation within round-off errors as one would expect from a finite-volume model.

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