Estimate of the truncation error of a finite volume discretisation of the Navier-Stokes equations on colocated grids

Alexandros Syrakos; Apostolos Goulas

doi:10.1002/fld.1038

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arXiv · 1508.02733

Estimate of the truncation error of a finite volume discretisation of the Navier-Stokes equations on colocated grids

Alexandros Syrakos·Apostolos Goulas

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Abstract

A methodology is proposed for the calculation of the truncation error of finite volume discretisations of the incompressible Navier-Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained on a given grid to a coarser grid and calculating the image of the discrete Navier-Stokes operator of the coarse grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretisations of the incompressible Navier-Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure-part of the mass fluxes is not dependent on the coefficients of the linearised momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two-dimensional flows, but extension to three-dimensional cases should not pose problems.

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Alexandros Syrakos, Apostolos Goulas. 2015-08-11. Estimate of the truncation error of a finite volume discretisation of the Navier-Stokes equations on colocated grids. https://doi.org/10.1002/fld.1038

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