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A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier–Stokes and Euler Equations on Unstructured Meshes

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Abstract

We propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier–Stokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution relaxation to speed-up the convergence and reduce the computation time. Numerical tests are provided to assess the effectiveness of the method to achieve up to sixth-order convergence rates. Simulations for the benchmark lid-driven cavity problem are also provided to highlight the benefit of the proposed high-order scheme.

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Acknowledgements

This research was financed by the International Centre for Mathematics and Computer Science in Toulouse–CIMI, by FEDER Funds through Programa Operational Fatores de Competitividade— COMPETE, and by Portuguese Funds FCT—Fundação para a Ciência e a Tecnologia, within the Projects PEst-C/MAT/UI0013/2014 and FCT-ANR/MAT-NAN/0122/2012.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062, Toulouse, France

    Ricardo Costa & Raphaël Loubère

  2. Centro de Matemática, Universidade do Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

    Ricardo Costa, Stéphane Clain & Gaspar J. Machado

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  1. Ricardo Costa
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  2. Stéphane Clain
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  4. Raphaël Loubère
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Correspondence to Stéphane Clain.

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Costa, R., Clain, S., Machado, G.J. et al. A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier–Stokes and Euler Equations on Unstructured Meshes. J Sci Comput 71, 1375–1411 (2017). https://doi.org/10.1007/s10915-016-0348-9

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