A kinetic flux-vector splitting method for single-phase and two-phase shallow flows

Zia, Saqib; Qamar, Shamsul

doi:10.1016/j.camwa.2014.01.015

Cited by 11 publications

(5 citation statements)

References 35 publications

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“…Moreover, this scheme can be extended to incompressible flow problems e.g. it can be extended to solve incompressible two-phase shallow flow model [ 12 ]. The suggested scheme is applied to both one and two-dimensional flow models.…”

Section: Introductionmentioning

confidence: 99%

Central Upwind Scheme for a Compressible Two-Phase Flow Model

et al. 2015

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In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

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Section: Introductionmentioning

confidence: 99%

Central Upwind Scheme for a Compressible Two-Phase Flow Model

et al. 2015

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“…To solve the Riemann equation, we compared the three high-performance numerical flux formulas: flux vector splitting (FVS) [26], flux difference splitting (FDS) [27], and the Osher scheme [28]. In this paper, we selected the FVS scheme, which has the merits of the finite difference method and finite element method, to improve the accuracy of the model.…”

Section: Methodsmentioning

confidence: 99%

Fluctuation of the Water Environmental Carrying Capacity in a Huge River-Connected Lake

Wang

Zhou

Tang

et al. 2015

IJERPH

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A new method, with the non-fully mixed coefficient (NFMC) considered, was put forward to calculate the water environmental carrying capacity (WECC) for huge river-connected lakes, of which the hydrological conditions always vary widely during a year. Poyang Lake, the most typical river-connected lake and the largest freshwater lake in China, was selected as the research area. Based on field investigations and numerical simulation, the monthly pollutant degradation coefficients and non-fully mixed coefficients of different lake regions were determined to explore the WECCs of COD, TN and TP of Poyang Lake in a common water year. It was found that under the hydrological conditions of a common water year the total WECCs of COD, TN and TP in the lake were respectively 181.9 × 104 t, 33.3 × 104 t and 1.86 × 104 t. Due to the varied lake water volume and self-purification ability, an evident temporal fluctuation of WECCs in Poyang Lake was observed. The dry seasons were characterized by a higher NFMCs but lower WECCs owing to the lower water level and degradation ability. Variation coefficients of COD and TN WECC were close to each other, of which the average level was about 58.5%, a little higher than that of TP.

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“…In statistical mechanics, the distribution of moving particles in the x - direction can be considered by local Maxwellian distribution function. The Maxwellian distribution function in normal direction n ∈ { x } is given as [ 22 , 46 ], where u n is the average fluid velocity in the n -direction, v n is the individual particle velocity in the same direction, and λ is the normalization factor of the distribution of random velocity. The transport of any flow quantity is due to the movement of particles.…”

Section: Kfvs Scheme For One-dimensional Single-phase Shallow Flow Momentioning

confidence: 99%

“…The remaining quantities, such as velocities in the y and z directions and water height may be treated as passive scalars moving with x-direction velocity of particles. Moreover, the current KFVS scheme can be easily extended to solve multidimensional incompressible and compressible multiphase flow models, see for example [ 39 , 46 ].…”

Section: Kfvs Scheme For Two-dimensional Single-phase Shallow Flow Momentioning

confidence: 99%

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A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

et al. 2018

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This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

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A kinetic flux-vector splitting method for single-phase and two-phase shallow flows

Cited by 11 publications

References 35 publications

Central Upwind Scheme for a Compressible Two-Phase Flow Model

Central Upwind Scheme for a Compressible Two-Phase Flow Model

Fluctuation of the Water Environmental Carrying Capacity in a Huge River-Connected Lake

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

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