Polynomial interpolation with repeated Richardson extrapolation to reduce discretization error in CFD

Marchi, Carlos Henrique; Martins, Márcio André; Novak, Leandro Alberto; Araki, Luciano Kiyoshi; Pinto, Márcio Augusto Villela; Gonçalves, Simone de Fátima Tomazzoni; Moro, Diego Fernando; Freitas, Inajara da Silva

doi:10.1016/j.apm.2016.05.029

Cited by 17 publications

(6 citation statements)

References 15 publications

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“…The basis for the approximation is the numerical error (difference between analytical and numerical solutions) or by estimating the error of the numerical solution. The effective order (based on the numerical error) is given by [18].…”

Section: Repeated Richardson Extrapolationmentioning

confidence: 99%

High Order of Accuracy for Poisson Equation Obtained by Grouping of Repeated Richardson Extrapolation with Fourth Order Schemes

Silva¹,

Rutyna²,

Righi³

et al. 2021

Computer Modeling in Engineering &Amp; Sciences

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In this article, we improve the order of precision of the two-dimensional Poisson equation by combining extrapolation techniques with high order schemes. The high order solutions obtained traditionally generate non-sparse matrices and the calculation time is very high. We can obtain sparse matrices by applying compact schemes. In this article, we compare compact and exponential finite difference schemes of fourth order. The numerical solutions are calculated in quadruple precision (Real * 16 or extended precision) in FORTRAN language, and iteratively obtained until reaching the round-off error magnitude around 1.0E−32. This procedure is performed to ensure that there is no iteration error. The Repeated Richardson Extrapolation (RRE) method combines numerical solutions in different grids, determining higher orders of accuracy. The main contribution of this work is based on a process that initializes with fourth order solutions combining with RRE in order to find solutions of sixth, eighth, and tenth order of precision. The multigrid Full Approximation Scheme (FAS) is also applied to accelerate the convergence and obtain the numerical solutions on the fine grids.

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Section: Repeated Richardson Extrapolationmentioning

confidence: 99%

High Order of Accuracy for Poisson Equation Obtained by Grouping of Repeated Richardson Extrapolation with Fourth Order Schemes

Silva¹,

Rutyna²,

Righi³

et al. 2021

Computer Modeling in Engineering &Amp; Sciences

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show abstract

“…After integrating twice and applying the BCs in the problems (36) and (37) , we come to the exact solution…”

Section: The Enate Schemementioning

confidence: 99%

“…Wang [36] gave a second-order exponential scheme for two-dimensional convectiondiffusion problems with just a five-point stencil, changing to fourth-order if Richardson extrapolation was applied. The effects of employing Richardson extrapolation in a CFD simulation are explored in [37] . A modern exponential scheme is given by Cui [38,39] where a Caputo time fractional model is presented for the unsteady transport equation.…”

Section: Introductionmentioning

confidence: 99%

Similarities and differences of two exponential schemes for convection-diffusion problems: The FV-CF and ENATE schemes

Llorente

Boonkkamp

Pascau

et al. 2020

Applied Mathematics and Computation

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“…represents higher-order terms in the polynomial. The Richardson extrapolation requires the use of at least three grid-levels (coarse, medium, and fine) [22,23,24], however, it is also possible to use an appropriately chosen number of grid-levels [25,26,27]. The refinement ratio r should be applied in each refinement step.…”

Section: Verification and Validation (Vandv) Assessmentmentioning

confidence: 99%

On the effect of the Froude number on the interface area of gravity-driven liquid rivulets

Sebastia‐Saez

Könözsy

et al. 2018

Chemical Engineering Research and Design

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Polynomial interpolation with repeated Richardson extrapolation to reduce discretization error in CFD

Cited by 17 publications

References 15 publications

High Order of Accuracy for Poisson Equation Obtained by Grouping of Repeated Richardson Extrapolation with Fourth Order Schemes

High Order of Accuracy for Poisson Equation Obtained by Grouping of Repeated Richardson Extrapolation with Fourth Order Schemes

Similarities and differences of two exponential schemes for convection-diffusion problems: The FV-CF and ENATE schemes

On the effect of the Froude number on the interface area of gravity-driven liquid rivulets

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