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

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• 作者：G.T. Oud^a ; ^{g.t.oud@tudelft.nl" class="auth_mail" title="E-mail the corresponding author} ; D.R. van der Heul^a ; C. Vuik^a ; R.A.W.M. Henkes^b
• 关键词：Incompressible flow ; Cylindrical coordinates ; Mimetic finite difference method ; Kinetic energy conservation
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：325
• 期：Complete
• 页码：314-337
• 全文大小：3634 K

文摘

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.