scholarly journals Second-order discontinuous Galerkin flood model: Comparison with industry-standard finite volume models

2021 ◽  
Vol 594 ◽  
pp. 125924
Author(s):  
Janice Lynn Ayog ◽  
Georges Kesserwani ◽  
James Shaw ◽  
Mohammad Kazem Sharifian ◽  
Domenico Bau
Keyword(s):  
Discontinuous Galerkin ◽  
Finite Volume ◽  
Model Comparison ◽  
Second Order ◽  
Industry Standard ◽  
Flood Model ◽  
Volume Models

scholarly journals Comparative analysis of hydrodynamics of treatment wetlands using finite volume models with empirical data

2014 ◽  
Vol 55 (13) ◽  
pp. 3587-3612 ◽  
Author(s):  
Rattandeep Singh ◽  
Sandeep Gupta ◽  
S. Raman ◽  
Prodyut Chakraborty ◽  
Puneet Sharma ◽  
...  
Keyword(s):  
Comparative Analysis ◽  
Finite Volume ◽  
Empirical Data ◽  
Treatment Wetlands ◽  
Volume Models

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.

scholarly journals Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations

2018 ◽  
Author(s):  
Tuomas Kärnä ◽  
Stephan C. Kramer ◽  
Lawrence Mitchell ◽  
David A. Ham ◽  
Matthew D. Piggott ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Unstructured Grid ◽  
Splitting Method ◽  
Time Integration ◽  
River Estuary ◽  
Coastal Ocean ◽  
Second Order ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Element Discretization

Abstract. Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to real life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability preserving time integration method and slope limiters. Compared to previous DG models advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.

Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations

2006 ◽  
Vol 13 (9) ◽  
pp. 753-770 ◽  
Author(s):  
Veselin A. Dobrev ◽  
Raytcho D. Lazarov ◽  
Panayot S. Vassilevski ◽  
Ludmil T. Zikatanov
Keyword(s):  
Discontinuous Galerkin ◽  
Elliptic Equations ◽  
Second Order ◽  
Galerkin Approximations ◽  
Second Order Elliptic Equations
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