Two-dimensional numerical modeling of dam-break flow using a new TVD finite-element scheme

A new numerical scheme based on the finite-element method with a total-variation-diminishing property is developed with the aim of studying the shock-capturing capability of the combination. The proposed model is formulated within the framework of the one-step Taylor–Galerkin scheme in conjunction w...

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Bibliographic Details
Published in:Journal of the Brazilian Society of Mechanical Sciences and Engineering Vol. 39; no. 11; pp. 4393 - 4401
Main Authors: Seyedashraf, Omid, Akhtari, Ali Akbar
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2017
Springer Nature B.V
Subjects:
Computational fluid dynamics
Engineering
Finite difference method
Finite element method
Fluid flow
Galerkin method
Mathematical models
Mechanical Engineering
Rarefaction
Shallow water equations
Smooth particle hydrodynamics
Supercritical flow
Technical Paper
Two dimensional models
Total-variation-diminishing
Shallow water equations
Taylor–Galerkin method
Dam-break flow
ISSN:1678-5878, 1806-3691
Online Access:Get full text
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Summary:A new numerical scheme based on the finite-element method with a total-variation-diminishing property is developed with the aim of studying the shock-capturing capability of the combination. The proposed model is formulated within the framework of the one-step Taylor–Galerkin scheme in conjunction with the Van Leer’s limiter function. The approach is applied to the two-dimensional shallow water equations by different test cases, i.e., the partial, circular, and one-dimensional dam-break flow problems. For the one-dimensional case, the sub- and supercritical flow regimes are considered. The results are compared with the analytical, finite-difference, and smoothed particle hydrodynamics solutions in the literature. The findings show that the proposed model can effectively mask the sources of errors in the abrupt changes of the flow conditions and is able to resolve the shock and rarefaction waves where other numerical models produce spurious oscillations.
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ISSN:1678-5878
1806-3691
DOI:10.1007/s40430-017-0776-y