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

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Abstract

A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are compared with the experimental data of two laboratory tests and with the results of other simulations carried out for the same tests by different authors. A comparison with the analytical solution of the oblique jump test has been also considered. Numerical results of the proposed scheme are in good agreement with measured data, as well as with analytical and higher order approximation methods results. The growth of the CPU time versus the cell number is investigated successively refining the elements of an initially coarse mesh. The CPU specific time, per element and per time step, is found out to be almost constant and no evidence of Courant–Friedrichs–Levi (CFL) number limitation has been detected in all the numerical experiments.
Lingua originaleEnglish
pagine (da-a)1253-1271
Numero di pagine19
RivistaAdvances in Water Resources
Volume30(5)
Stato di pubblicazionePublished - 2007

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shallow-water equation
decomposition
methodology
prediction
simulation
experiment
test
refining

All Science Journal Classification (ASJC) codes

  • Water Science and Technology

Cita questo

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title = "A marching in space and time (MAST) solver of the shallow water equations. Part II: the 2D model.",
abstract = "A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are compared with the experimental data of two laboratory tests and with the results of other simulations carried out for the same tests by different authors. A comparison with the analytical solution of the oblique jump test has been also considered. Numerical results of the proposed scheme are in good agreement with measured data, as well as with analytical and higher order approximation methods results. The growth of the CPU time versus the cell number is investigated successively refining the elements of an initially coarse mesh. The CPU specific time, per element and per time step, is found out to be almost constant and no evidence of Courant–Friedrichs–Levi (CFL) number limitation has been detected in all the numerical experiments.",
author = "Carmelo Nasello and Costanza Arico' and Tullio Tucciarelli",
year = "2007",
language = "English",
volume = "30(5)",
pages = "1253--1271",
journal = "Advances in Water Resources",
issn = "0309-1708",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - A marching in space and time (MAST) solver of the shallow water equations. Part II: the 2D model.

AU - Nasello, Carmelo

AU - Arico', Costanza

AU - Tucciarelli, Tullio

PY - 2007

Y1 - 2007

N2 - A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are compared with the experimental data of two laboratory tests and with the results of other simulations carried out for the same tests by different authors. A comparison with the analytical solution of the oblique jump test has been also considered. Numerical results of the proposed scheme are in good agreement with measured data, as well as with analytical and higher order approximation methods results. The growth of the CPU time versus the cell number is investigated successively refining the elements of an initially coarse mesh. The CPU specific time, per element and per time step, is found out to be almost constant and no evidence of Courant–Friedrichs–Levi (CFL) number limitation has been detected in all the numerical experiments.

AB - A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are compared with the experimental data of two laboratory tests and with the results of other simulations carried out for the same tests by different authors. A comparison with the analytical solution of the oblique jump test has been also considered. Numerical results of the proposed scheme are in good agreement with measured data, as well as with analytical and higher order approximation methods results. The growth of the CPU time versus the cell number is investigated successively refining the elements of an initially coarse mesh. The CPU specific time, per element and per time step, is found out to be almost constant and no evidence of Courant–Friedrichs–Levi (CFL) number limitation has been detected in all the numerical experiments.

UR - http://hdl.handle.net/10447/9387

M3 - Article

VL - 30(5)

SP - 1253

EP - 1271

JO - Advances in Water Resources

JF - Advances in Water Resources

SN - 0309-1708

ER -