Development and testing of a simple 2D finite volume model of sub-critical shallow water flow

2004 ◽  
Vol 44 (11) ◽  
pp. 1231-1255 ◽  
Author(s):  
Matthew Horritt
Keyword(s):  
Shallow Water ◽  
Water Flow ◽  
Finite Volume ◽  
Shallow Water Flow ◽  
Finite Volume Model ◽  
Volume Model

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.

GPU computing for shallow water flow simulation based on finite volume schemes

2011 ◽  
Vol 339 (2-3) ◽  
pp. 165-184 ◽  
Author(s):  
Manuel J. Castro ◽  
Sergio Ortega ◽  
Marc de la Asunción ◽  
José M. Mantas ◽  
José M. Gallardo
Keyword(s):  
Shallow Water ◽  
Water Flow ◽  
Finite Volume ◽  
Gpu Computing ◽  
Flow Simulation ◽  
Finite Volume Schemes ◽  
Shallow Water Flow ◽  
Simulation Based
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