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A fully conservative mimetic discretization of the Navier–Stokes equations in cylindrical coordinates with associated singularity treatment. / Oud, Guido; van der Heul, Duncan; Vuik, Kees; Henkes, Ruud.

In: Journal of Computational Physics, Vol. 325, 2016, p. 314-337.

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@article{b9c6eb377f804f6e83c2d1a0ae810d2b,
title = "A fully conservative mimetic discretization of the Navier–Stokes equations in cylindrical coordinates with associated singularity treatment",
abstract = "We present a finite difference discretization of the incompressible Navier–Stokes equations in cylindrical coordinates. This currently is, to the authors' knowledge, the only scheme available that is demonstrably capable of conserving mass, momentum and kinetic energy (in the absence of viscosity) on both uniform and non-uniform grids. Simultaneously, we treat the inherent discretization issues that arise due to the presence of the coordinate singularity at the polar axis. We demonstrate the validity of the conservation claims by performing a number of numerical experiments with the proposed scheme, and we show that it is second order accurate in space using the Method of Manufactured Solutions.",
keywords = "Incompressible flow, Cylindrical coordinates, Mimetic finite difference method, Kinetic energy conservation",
author = "Guido Oud and {van der Heul}, Duncan and Kees Vuik and Ruud Henkes",
year = "2016",
doi = "10.1016/j.jcp.2016.08.038",
language = "English",
volume = "325",
pages = "314--337",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - A fully conservative mimetic discretization of the Navier–Stokes equations in cylindrical coordinates with associated singularity treatment

AU - Oud, Guido

AU - van der Heul, Duncan

AU - Vuik, Kees

AU - Henkes, Ruud

PY - 2016

Y1 - 2016

N2 - We present a finite difference discretization of the incompressible Navier–Stokes equations in cylindrical coordinates. This currently is, to the authors' knowledge, the only scheme available that is demonstrably capable of conserving mass, momentum and kinetic energy (in the absence of viscosity) on both uniform and non-uniform grids. Simultaneously, we treat the inherent discretization issues that arise due to the presence of the coordinate singularity at the polar axis. We demonstrate the validity of the conservation claims by performing a number of numerical experiments with the proposed scheme, and we show that it is second order accurate in space using the Method of Manufactured Solutions.

AB - We present a finite difference discretization of the incompressible Navier–Stokes equations in cylindrical coordinates. This currently is, to the authors' knowledge, the only scheme available that is demonstrably capable of conserving mass, momentum and kinetic energy (in the absence of viscosity) on both uniform and non-uniform grids. Simultaneously, we treat the inherent discretization issues that arise due to the presence of the coordinate singularity at the polar axis. We demonstrate the validity of the conservation claims by performing a number of numerical experiments with the proposed scheme, and we show that it is second order accurate in space using the Method of Manufactured Solutions.

KW - Incompressible flow

KW - Cylindrical coordinates

KW - Mimetic finite difference method

KW - Kinetic energy conservation

U2 - 10.1016/j.jcp.2016.08.038

DO - 10.1016/j.jcp.2016.08.038

M3 - Article

VL - 325

SP - 314

EP - 337

JO - Journal of Computational Physics

T2 - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -

ID: 9189935