A mass conservative scheme for simulating shallow flows over variable topographies using unstructured grid

Mohamadian, Ali; Roux, Daniel Y. Le; Tajrishi, M; Mazaheri, K.

doi:10.1016/j.advwatres.2004.10.006

Cited by 23 publications

(20 citation statements)

References 22 publications

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“…Mohammadian et al [10], have shown that scheme (12) for the di usive uxes, leads to correct simulation of circulating zones. The convective uxes F are calculated here by a Godunov-type scheme…”

Section: Finite Volume Methods On Unstructured Gridsmentioning

confidence: 97%

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Simulation of shallow flows over variable topographies using unstructured grids

Mohammadian

Roux

2006

Numerical Methods in Fluids

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SUMMARYSimulation of shallow ows over variable topographies is a challenging case for most available shockcapturing schemes. This problem arises because the source terms and ux gradients are not balanced in the numerical computations. Treatments for this problem generally work well on structured grids, but they are usually too expensive, and most of them are not directly applicable to unstructured grids. In this paper we propose two e cient methods to treat the source terms without upwinding and to satisfy the compatibility condition on unstructured grids. In the ÿrst method, the calculation of the bed slope source term is performed by employing a compatible approximation of water depth at the cell interfaces. In the second one, di erent components of the bed slope term are considered separately and a compatible discretization of the components is proposed. The present treatments are applicable for most schemes including the Roe's method without changing the performance of the original scheme for smooth topographies.

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Section: Finite Volume Methods On Unstructured Gridsmentioning

confidence: 97%

“…The application of Gauss theorem to the di usive and convective ux integrals gives (10) and the boundary integral is approximated by a summation over the triangle edges…”

Section: Finite Volume Methods On Unstructured Gridsmentioning

confidence: 99%

Simulation of shallow flows over variable topographies using unstructured grids

Mohammadian

Roux

2006

Numerical Methods in Fluids

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“…The TVD scheme is a one-dimensional version of the two-dimensional scheme that Unami et al (2009) has developed with an extension of the flux splitting scheme by Liou and Steffen (1993). A surface gradient method (SGM) (Mohamadian et al 2004) is also employed. On the other hand, the finite element method with the fully upwind scheme is applied for discretizing the KBE (11) with (7) and (12).…”

Section: Methodsmentioning

confidence: 99%

A stochastic model for behaviour of fish ascending an agricultural drainage system

Unami

Ishida

Kawachi

et al. 2009

Paddy Water Environ

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Adults of Carassius auratus grandoculis ascend from Lake Biwa, Japan, into riparian paddy fields via agricultural drainage systems for the purpose of spawning. However, land improvement works conducted in the second half of the twentieth century have brought about obstacles for passage of the fish, and several restoration projects to recover the migratory environment are being attempted. A continuous Markov process model is presented to scientifically support such a project, defining an ascending probability that quantitatively assesses the ability of an agricultural drainage system with hydraulic structures for the ascent of the fish. Computational methods are developed to numerically obtain flow fields of the agricultural drainage system and then the ascending probability in the entire spatio-temporal domain. The values of model parameters are deductively inferred, referring to results of field observations. From the computational results of the ascending probability in the agricultural drainage system, effects of hydraulic structures allowing ascent of the fish are clarified.

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“…Upwind finite volume schemes have been successfully employed for the simulation of some challenging problems for shallow flows such as dam break flows over dry and irregular topographies (e.g. [4][5][6][7][8]). …”

Section: Introductionmentioning

confidence: 99%

Numerical approximation of viscous terms in finite volume models for shallow waters

Mohammadian¹

2009

Numerical Methods in Fluids

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SUMMARYTwo methods for the numerical treatment of viscous terms in shallow water equations are studied and computational details are given for structured grids. It is demonstrated that the first scheme, which is widely used, may lead to spurious oscillations arising from computational modes. In fact, the shortest resolvable waves of wave length 2 x are invisible to this method. The second method, although more expensive, is free of computational modes and it presents a more accurate approximation of viscous terms. The dispersion relation of the second method is closer to the analytical case and it has a smaller truncation error, which is due to the fact that it uses a more localized control volume. Numerical experiments are also presented that support the study.

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A mass conservative scheme for simulating shallow flows over variable topographies using unstructured grid

Cited by 23 publications

References 22 publications

Simulation of shallow flows over variable topographies using unstructured grids

Simulation of shallow flows over variable topographies using unstructured grids

A stochastic model for behaviour of fish ascending an agricultural drainage system

Numerical approximation of viscous terms in finite volume models for shallow waters

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