The Finite Volume Method

Moukalled, F.; Mangani, Luca; Darwish, M.

doi:10.1007/978-3-319-16874-6_5

Cited by 79 publications

(34 citation statements)

References 7 publications

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“…Figures 6 and 7 illustrate the evolution of computed solutions of the water depth (left) and the scalar concentration (right). The results of this numerical tests using the proposed numerical scheme are comparable with those of previous studies [34,3,42,2,32]). As shown in these figures at time t = 2, the water reaches the two smaller humps, and the front of the zone with solute concentration is still located approximately at x = 10.…”

Section: Example 5: Pollutant Transport Over Complex Bottom Topographysupporting

confidence: 86%

“…Here we perform a numerical test which is widely used in previous studies [2,3,34,42,32] as a benchmark utilized to measure the performance of numerical models to simulate problems involving flows with scalar transport over wet/dry areas. In this numerical example, the computational domain [0, 75] × [−15, 15] and we consider a 2-D dam-break located at x = 16 with still water in the initial condition in which the water depth h = 1.875 is used upstream the dam, whereas downstream the dam the water depth is set to zero.…”

Section: Example 5: Pollutant Transport Over Complex Bottom Topographymentioning

confidence: 99%

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A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport

Karjoun¹,

Beljadid²,

LeFloch³

2020

Preprint

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We develop a new finite volume method using unstructured mesh-vertex grids for coupled systems modeling shallow water flows and solute transport over complex bottom topography. Novel well-balanced positivity preserving discretization techniques are proposed for the water surface elevation and the concentration of the pollutant. For the hydrodynamic system, the proposed scheme preserves the steady state of a lake at rest and the positivity of the water depth. For the scalar transport equation, the proposed method guarantees the positivity and a perfect balance of the scalar concentration. The constant-concentration states are preserved in space and time for any hydrodynamic field and complex topography in the absence of source terms of the passive pollutant. Importantly and this is one of the main features of our approach is that the novel reconstruction techniques proposed for the water surface elevation and concentration satisfy the discrete maximum-minimum principle for the solute concentration. We demonstrate, in a series of numerical tests, the well-balanced and positivity properties of the proposed method and the accuracy of our techniques and their potential advantages in predicting the solutions of the shallow water-transport model.

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Section: Example 5: Pollutant Transport Over Complex Bottom Topographysupporting

confidence: 86%

Section: Example 5: Pollutant Transport Over Complex Bottom Topographymentioning

confidence: 99%

A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport

Karjoun¹,

Beljadid²,

LeFloch³

2020

Preprint

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“…OpenFOAM finite volume method (FVM) is used to calculate the fluid flow [20,21]. In the finite volume method, the values of flow variables are stored at the center of each control volume.…”

Section: Governing Equationsmentioning

confidence: 99%

The ground effect on flapping Bio and NACA 0015 airfoils in power extraction and propulsion regimes

Sarbandi

Naderi

Parhizkar

2020

J Braz. Soc. Mech. Sci. Eng.

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In this study, the heaving and pitching motions of a biologically inspired airfoil (Bio airfoil) and a NACA 0015 airfoil in power extraction ( Po ) and propulsion ( Pr ) operating regimes are numerically simulated considering the ground effect. The effect of the mean distance of the flapping airfoil to the ground surface on the aerodynamic coefficients, Po and Pr efficiency, is investigated. The simulation is done at Reynolds number of 1100, using overset mesh capability of OpenFOAM. Mean distance from airfoil center of rotation to the ground surface varies from 1.25 to 4 times of airfoil's chord length, c. Motion parameters such as heaving and pitching amplitudes and their phase difference are kept constant at 1c, ∕4 , and ∕2 , respectively. The reduced frequency of the motion is selected 0.1 or 0.2. The obtained results show that the change in the distance to the ground does not change the nature of the operating regimes. In the Po regime, the Po efficiency of the Bio airfoil decreases with an increase in mean distance to the ground; however, it slightly changes for NACA 0015 airfoil. In the Po regime, the Bio airfoil has a higher efficiency than NACA 0015 airfoil. Due to the ground help, the leading edge vortex increases Po efficiency only on Bio airfoil. In the Pr regime, the Pr efficiency of both airfoils decreases with an increase in the distance to the ground, and NACA 0015 airfoil has a higher efficiency than Bio airfoil.

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“…To avoid these problems, in this work, the finite volume method [46] is introduced to discretize the diffusion term. As shown in Fig.…”

Section: Discrete Schemes For the Energy Equationmentioning

confidence: 99%

2D Simulation of boiling heat transfer on the wall with an improved hybrid lattice Boltzmann model

Liu

2019

Applied Thermal Engineering

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The Finite Volume Method

Cited by 79 publications

References 7 publications

A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport

A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport

The ground effect on flapping Bio and NACA 0015 airfoils in power extraction and propulsion regimes

2D Simulation of boiling heat transfer on the wall with an improved hybrid lattice Boltzmann model

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