A finite element method for 3D hydrostatic water flows

Fontana, Lorenzo; Miglio, Edie; Quarteroni, Alfio; Saleri, Fausto

doi:10.1007/s007910050031

Cited by 11 publications

(8 citation statements)

References 11 publications

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“…In addition, approaching the time period (t = 500 and 600 s) the velocity field changes the direction pointing towards the channel entrance. Similar flow features have been observed in published references in the literature, compare for instance [17,27]. Note that the performance of the ENOSLAG method is very attractive since the computed solutions remain stable and oscillation-free even for relatively coarse grids without solving non-linear systems or requiring very small timesteps.…”

Section: Recirculation Flow Problemsupporting

confidence: 69%

“…We also compare numerical results obtained using the conventional SLAG method with those computed using the ENOSLAG method for this example. Notice that, we denote by SLAG the conventional SLAG method obtained by setting n j = 1 in (27), while by ENOSLAG we refer to the ENOSLAG method with the correction (27)- (28). As a second example, we consider the recirculation flow in a channel with forwardfacing step.…”

Section: Numerical Results and Examplesmentioning

confidence: 99%

“…This example consists on simulating the recirculation flow in a channel with forward-facing step studied in [17,27] among others. Here, we solve the Equations (8) on flat bottom (i.e.…”

Section: Recirculation Flow Problemmentioning

confidence: 99%

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An essentially non‐oscillatory semi‐Lagrangian method for tidal flow simulations

El‐Amrani

Seaı̈d

2009

Numerical Meth Engineering

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SUMMARYWe develop an essentially non-oscillatory semi-Lagrangian method for solving two-dimensional tidal flows. The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions, eddy viscosity, wind shear stresses and Coriolis forces. The method employs the modified method of characteristics to discretize the convective term in a finite element framework. Limiters are incorporated in the method to reconstruct an essentially non-oscillatory algorithm at minor additional cost. The central idea consists in combining linear and quadratic interpolation procedures using nodes of the finite element where departure points are localized. The resulting semidiscretized system is then solved by an explicit Runge-Kutta Chebyshev scheme with extended stages. This scheme adds in a natural way a stabilizing stage to the conventional Runge-Kutta method using the Chebyshev polynomials. The proposed method is verified for the recirculation tidal flow in a channel with forward-facing step. We also apply the method for simulation of tidal flows in the Strait of Gibraltar. In both test problems, the proposed method demonstrates its ability to handle the interaction between water free-surface and bed frictions.

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Section: Recirculation Flow Problemsupporting

confidence: 69%

Section: Numerical Results and Examplesmentioning

confidence: 99%

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An essentially non‐oscillatory semi‐Lagrangian method for tidal flow simulations

El‐Amrani

Seaı̈d

2009

Numerical Meth Engineering

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“…[7]). Note that we have neglected the fluid viscosity in (2.1), an assumption that is often admissible in practical situations (see, e.g., [8,12,10]). In order to properly take into account the hyperbolic nature of system (2.1), characteristic-based time discretizations are widely used for the shallow water equaDownloaded 12/30/12 to 138.26.31.3.…”

Section: The Shallow Water Equations and Methods Of Characteristicsmentioning

confidence: 99%

“…For the Raviart-Thomas mixed finite element method employed in [8,12], this mass balance error is zero (up to interpolation errors forĤ old on the current triangulation). In our least squares approach M(H h , u h ) does not vanish, in general, but it is rather small, and decreases with refinement, as illustrated by the numerical results in the next section.…”

Section: Finite Element Discretization Approximate Mass Balance Andmentioning

confidence: 98%

A First-Order System Least Squares Finite Element Method for the Shallow Water Equations

Starke¹

2005

SIAM J. Numer. Anal.

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A least squares finite element method for the first-order system of the shallow water equations is proposed and studied. The method combines a characteristic-based time discretization with a least squares finite element approach which approximates the water level and the velocity field in H 1 and H(div), respectively. The linearized least squares functional is shown to be elliptic, uniformly as the time-step size τ approaches zero, with respect to a suitably weighted norm. Moreover, Lipschitz continuity of the Fréchet derivative is shown with respect to this norm. This implies that the local evaluation of the nonlinear least squares functional constitutes an a posteriori error estimator on which an adaptive refinement technique may be based. The efficiency of such an adaptive finite element approach is tested numerically for a test problem involving the surface flow in a widening channel leading to a recirculating velocity field.

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Parallel Computing for the Simulation of 3D Free Surface Flows in Environmental Applications

Causin

Miglio

2002

Recent Advances in Parallel Virtual Machine and Message Passing Interface

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The numerical simulation of 3D free surface flows in environmental fluid-dynamics requires a huge computational effort. In this work we address the numerical aspects and the computer implementation of the parallel finite element code Stratos for the solution of medium and large scale hydrodynamics problems. The code adopts the MPI protocol to manage inter-processor communication. Particular attention is paid to present some original details of the software implementation as well as to show the numerical results obtained on a Cray T3E machine.

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A finite element method for 3D hydrostatic water flows

Cited by 11 publications

References 11 publications

An essentially non‐oscillatory semi‐Lagrangian method for tidal flow simulations

An essentially non‐oscillatory semi‐Lagrangian method for tidal flow simulations

A First-Order System Least Squares Finite Element Method for the Shallow Water Equations

Parallel Computing for the Simulation of 3D Free Surface Flows in Environmental Applications

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