An improved r-factor algorithm for TVD schemes

Li, Lianxia; Liao, Huasheng; Liu, Qi

doi:10.1016/j.ijheatmasstransfer.2007.04.051

Cited by 37 publications

(58 citation statements)

References 16 publications

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“…Herein lies the main difficulty of implementing TVD schemes on unstructured mesh, and a few suggestions have been offered in the literature [50,51]. We successfully implemented a technique recently suggested [52] to evaluate r-factor. Shown in Fig.…”

Section: And ð25þmentioning

confidence: 99%

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

Patil

Lakshmisha

2009

Journal of Computational Physics

112

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Section: And ð25þmentioning

confidence: 99%

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

Patil

Lakshmisha

2009

Journal of Computational Physics

112

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“…Li et al [8] erroneously state that Eq. (9) misrepresents the gradient ratio if the variation in φ is exponential.…”

Section: Upwind Value On Unstructured Meshesmentioning

confidence: 99%

“…This is a simplification of the multidimensional applications typically found in heat and mass transfer as well as fluid dynamics. Furthermore, the non-linearity inherently introduced by TVD differencing [7], since the choice of differencing scheme is dependent on the advected scalar field, is a frequently overlooked issue in the relevant literature, even though oscillations caused by compressive TVD schemes reported in previous studies [8][9][10][11] may be attributed to this non-linearity.…”

Section: Introductionmentioning

confidence: 99%

“…Both approximations reconstruct the upwind value exactly on one-dimensional, equidistant meshes, yet this reconstruction becomes unreliable and possibly erroneous on non-equidistant meshes and non-rectilinear meshes. Other methods to extrapolate the upwind node on unstructured meshes, albeit less frequently encountered in the literature, have been proposed by Jasak et al [14], Li et al [8] and Zhang et al [15]. Another common problem with the application of unstructured meshes is that the cells are typically not arranged equidistant to each other, which requires special care when face values are interpolated from values at adjacent cell centres.…”

Section: Introductionmentioning

confidence: 99%

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TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness

Denner

Wachem

2015

Journal of Computational Physics

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Total variation diminishing (TVD) schemes are a widely applied group of monotonicitypreserving advection differencing schemes for partial differential equations in numerical heat transfer and computational fluid dynamics. These schemes are typically designed for one-dimensional problems or multidimensional problems on structured equidistant quadrilateral meshes. Practical applications, however, often involve complex geometries that cannot be represented by Cartesian meshes and, therefore, necessitate the application of unstructured meshes, which require a more sophisticated discretisation to account for their additional topological complexity. In principle, TVD schemes are applicable to unstructured meshes, however, not all the data required for TVD differencing is readily available on unstructured meshes, and the solution suffers from considerable numerical diffusion as a result of mesh skewness. In this article we analyse TVD differencing on unstructured three-dimensional meshes, focusing on the non-linearity of TVD differencing and the extrapolation of the virtual upwind node. Furthermore, we propose a novel monotonicity-preserving correction method for TVD schemes that significantly reduces numerical diffusion caused by mesh skewness. The presented numerical experiments demonstrate the importance of accounting for the non-linearity introduced by TVD differencing and of imposing carefully chosen limits on the extrapolated virtual upwind node, as well as the efficacy of the proposed method to correct mesh skewness.

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“…air mass movement in the atmosphere [1,2], and transport of pollutant and sediment in environmental flows [3][4][5]. In numerical simulations, the advection is hard to cope with due to its hyperbolic property [6,7], and may induce numerical errors such as numerical diffusion and oscillations, especially near the discontinuous parts of the solution [8][9][10]. Generally speaking, numerical diffusion is a result of low order schemes, while numerical oscillations are attributed to the higher order schemes as limiters [11].…”

Section: Introductionmentioning

confidence: 99%

Numerical error control for second-order explicit TVD scheme with limiters in advection simulation

Hou

Liang

et al. 2015

Computers & Mathematics with Applications

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An improved r-factor algorithm for TVD schemes

Cited by 37 publications

References 16 publications

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness

Numerical error control for second-order explicit TVD scheme with limiters in advection simulation

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