A marching in space and time (MAST) solver of the shallow water equations. Part II: The 2D model

Aricò, Costanza; Nasello, Carmelo; Tucciarelli, Tullio

doi:10.1016/j.advwatres.2006.11.004

Cited by 21 publications

(120 citation statements)

References 31 publications

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“…However, the advantage of the inclusion of this corrective step has never been validated in the previous papers Tucciarelli, 2007a, Aricò et al, 2007 ) with numerical experiments. To limit the computational burden of this additional step, in the present work we propose a new and computationally less burdensome cell ordering procedure, compared with the ones proposed in Aricò et al (2007 ) and Aricò et al (2013a ), respectively.…”

Section: Main Motivations Of the Present Workmentioning

confidence: 99%

“…The prediction step of the hydrostatic problem is solved in its integral form, while the diffusive corrector step is solved by integrating its linearized form Aricò and Tucciarelli (2007a ), Aricò et al (2007 ).…”

Section: The Prediction-correction Procedures Of the Hydrostatic Problemmentioning

confidence: 99%

“…We solve the prediction step of the hydrostatic problem by applying the MAST procedure ( Aricò and Tucciarelli, 2007a, Aricò et al, 2007, 2013a. Key aspects of such a procedure are as follows (see Fig.…”

Section: The Prediction-correction Procedures Of the Hydrostatic Problemmentioning

confidence: 99%

“…Key aspects of such a procedure are as follows (see Fig. 3 ): (1) the cell ordering at the beginning of each time iteration, according to certain criteria (further specified), and 2) the sequential solution of the computational cells after their ordering ( Aricò and Tucciarelli, 2007a, Aricò et al, 2007, 2013a. This procedure has been originally applied for potential flow problems.…”

Section: The Prediction-correction Procedures Of the Hydrostatic Problemmentioning

confidence: 99%

“…We use the MArching in Space and Time (MAST) procedure ( Aricò and Tucciarelli, 2007a;Aricò et al, 2007Aricò et al, , 2013a to solve the hydrostatic prediction problem. The computational cells are sequentially solved throughout the domain after their ordering at the beginning of each time iteration.…”

Section: Introductionmentioning

confidence: 99%

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A non-hydrostatic pressure distribution solver for the nonlinear shallow water equations over irregular topography

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Section: Main Motivations Of the Present Workmentioning

confidence: 99%

Section: The Prediction-correction Procedures Of the Hydrostatic Problemmentioning

confidence: 99%

Section: The Prediction-correction Procedures Of the Hydrostatic Problemmentioning

confidence: 99%

Section: The Prediction-correction Procedures Of the Hydrostatic Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hydraulic Conditions of Flood Wave Propagation in the Valley of the Narew River after the Siemianówka Dam Overtopping Failure

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A marching in space and time (MAST) solver of the shallow water equations. Part I: The 1D model

Aricò

Tucciarelli

2007

Advances in Water Resources

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A new approach is presented for the numerical solution of the complete 1D Saint-Venant equations. At each time step, the governing system of partial differential equations (PDEs) is split, using a fractional time step methodology, into a convective prediction system and a diffusive correction system. Convective prediction system is further split into a convective prediction and a convective correction system, according to a specified approximated potential. If a scalar exact potential of the flow field exists, correction vanishes and the solution of the convective correction system is the same solution of the prediction system. Both convective prediction and correction systems are shown to have at each x À t point a single characteristic line, and a corresponding eigenvalue equal to the local velocity. A marching in space and time (MAST) technique is used for the solution of the two systems. MAST solves a system of two ordinary differential equations (ODEs) in each computational cell, using for the time discretization a self-adjusting fraction of the original time step. The computational cells are ordered and solved according to the decreasing value of the potential in the convective prediction step and to the increasing value of the same potential in the convective correction step. The diffusive correction system is solved using an implicit scheme, that leads to the solution of a large linear system, with the same order of the cell number, but sparse, symmetric and well conditioned. The numerical model shows unconditional stability with regard of the Courant-Friedrichs-Levi (CFL) number, requires no special treatment of the source terms and a computational effort almost proportional to the cell number. Several tests have been carried out and results of the proposed scheme are in good agreement with analytical solutions, as well as with experimental data.

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A marching in space and time (MAST) solver of the shallow water equations. Part II: The 2D model

Cited by 21 publications

References 31 publications

A non-hydrostatic pressure distribution solver for the nonlinear shallow water equations over irregular topography

A non-hydrostatic pressure distribution solver for the nonlinear shallow water equations over irregular topography

Hydraulic Conditions of Flood Wave Propagation in the Valley of the Narew River after the Siemianówka Dam Overtopping Failure

A marching in space and time (MAST) solver of the shallow water equations. Part I: The 1D model

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