Assessment of different reconstruction techniques for implementing the NVSF schemes on unstructured meshes

Zhang, Di; Jiang, Chen; Chen, Yang; Yang, Yan

doi:10.1002/fld.3846

Cited by 17 publications

(28 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Prescribed velocity fields are used and the accuracy is quantitatively measured by the average L 2 norm of the difference between the exact and numerical solutions:

E = \frac{1}{N} \cdot italicSqrt ((), \sum_{i = 1}^{N} {((), q_{i}^{n} - q_{i}^{a})}^{2})

where

q_{i}^{n}

is the calculated solution after n time steps,

q_{i}^{a}

is the exact analytical solution, and N is the number of control volumes .…”

Section: Numerical Test Casesmentioning

confidence: 99%

“…Darwish's r-factor algorithm. It is apparent that the main difficulty in implementing TVD schemes on an arbitrary unstructured mesh lies in the need for defining a virtual far-upwind node U. Darwish and Moukalled [38] proposed the so-called exact r-factor technique, which is broadly used to resolve this issue in the literature [1,2,6,33,38,39,[43][44][45][46]]. Darwish's r-factor formulation can be written as follows:…”

Section: Extrapolation R-factor Algorithmsmentioning

confidence: 99%

“…It is not straightforward to extend TVD schemes into arbitrary unstructured grids because of this reason, which is especially challenging for three-dimensional problems. Although a large number of TVD schemes have been proposed and analyzed, little attention has been paid to implementing these schemes on arbitrary unstructured grids, partly because of the complexity of locating the far-upstream nodes and determining the variable values there [1][2][3]6,33,38,39,[43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

“…FFISAM), being suitable for arbitrary unstructured grids, is proposed and benchmarked in several two-dimensional (2D) advection test problems. Its performance is compared with several existing algorithms, such as Darwish's and Hou's algorithms [1][2][3]6,33,38,39,[43][44][45][46]].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A refined r‐factor algorithm for TVD schemes on arbitrary unstructured meshes

Zhang

Jiang

Cheng

et al. 2015

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

SUMMARYA refined r-factor algorithm for implementing total variation diminishing (TVD) schemes on arbitrary unstructured meshes, referred to henceforth as a face-perpendicular far-upwind interpolation scheme for arbitrary meshes (FFISAM), is proposed based on an extensive review of the existing r-factor algorithms available in the literature. The design principles, as well as the respective advantages and disadvantages, of the existing algorithms are first systematically analyzed before presenting the FFISAM. The FFISAM is designed to combine the merits of various existing r-factor algorithms. The performance of the FFISAM, implemented in 10 classical TVD schemes, is evaluated against four two-dimensional pure-advection benchmark test cases where analytical solutions are available. The numerical results clearly show that the FFISAM leads to a better overall performance than the existing algorithms in terms of accuracy and convergence on arbitrary unstructured meshes for the 10 classical TVD schemes.

show abstract

“…Prescribed velocity fields are used and the accuracy is quantitatively measured by the average L 2 norm of the difference between the exact and numerical solutions:

E = \frac{1}{N} \cdot italicSqrt ((), \sum_{i = 1}^{N} {((), q_{i}^{n} - q_{i}^{a})}^{2})

where

q_{i}^{n}

is the calculated solution after n time steps,

q_{i}^{a}

is the exact analytical solution, and N is the number of control volumes .…”

Section: Numerical Test Casesmentioning

confidence: 99%

Section: Extrapolation R-factor Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A refined r‐factor algorithm for TVD schemes on arbitrary unstructured meshes

Zhang

Jiang

Cheng

et al. 2015

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…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: 97%

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

Denner

Wachem

2015

Journal of Computational Physics

View full text Add to dashboard Cite

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.

show abstract

A Group of CFL-Dependent Flux-Limiters to Control the Numerical Dissipation in Multi-stage Unsteady Calculation

Ren

Wang

2019

J Sci Comput

View full text Add to dashboard Cite

In this paper, a group of CFL-dependent Piecewise-Linear flux-limiters termed as GPL-CFL limiters are proposed to control and limit the numerical dissipation in Multi-stage Unsteady high resolution schemes. These limiters satisfy the second-order TVD criterion while are subject to the Multi-stage Time-space separated Unsteady TVD criterion. The accuracy of the high resolution schemes using these limiters can be improved by properly tuning the four parameters including CFL number and other three variables contained in them. To fully illustrate the ability of GPL-CFL limiters to control dissipation, an entropy dissipation function with these limiters is defined and is proved to be monotonic with each parameter. For some endpoint values of parameters, a relatively ideal limiter named by MDF-CFL limiter is obtained in the sense of CFL-dependent minimum dissipation. In the end, the high resolution entropy-consistent schemes which are termed as HRECSIS schemes are constructed using GPL-CFL limiters and are used to compute the solutions for Burgers and Euler equations in 1D and 2D cases. Numerical results sufficiently illustrate the accuracy of HRECSIS schemes, in the context of MTU calculations, are closely related with the four parameters contained in GPL-CFL limiters and the higher resolution than their corresponding CFL-independent flux-limiters can be obtained for computed solutions when CFL number is in the range of (0, 0.5).

show abstract

Assessment of different reconstruction techniques for implementing the NVSF schemes on unstructured meshes

Cited by 17 publications

References 32 publications

A refined r‐factor algorithm for TVD schemes on arbitrary unstructured meshes

A refined r‐factor algorithm for TVD schemes on arbitrary unstructured meshes

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

A Group of CFL-Dependent Flux-Limiters to Control the Numerical Dissipation in Multi-stage Unsteady Calculation

Contact Info

Product

Resources

About