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On generalised penalty approaches for slip, free surface and related boundary conditions in viscous flow simulation

Yvonne Stokes (School of Mathematical Sciences, The University of Adelaide, Adelaide, Australia)
Graham Carey (College of Engineering, University of Texas at Austin, Austin, Texas, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 9 August 2011

Abstract

Purpose

The purpose of this paper is to extend the penalty concept to treat partial slip, free surface, contact and related boundary conditions in viscous flow simulation.

Design/methodology/approach

The penalty partial‐slip formulation is analysed and related to the classical Navier slip condition. The same penalty scheme also allows partial penetration through a boundary, hence the implementation of porous wall boundaries. The finite element method is used for investigating and interpreting penalty approaches to boundary conditions.

Findings

The generalised penalty approach is verified by means of a novel variant of the circular‐Couette flow problem, having partial slip on one of the cylindrical boundaries, for which an analytic solution is derived. Further verificationis provided by consideration of viscous flow over a sphere with partial slip on the surface, and comparison of numerical and classical solutions. Numerical studies illustrate the versatility of the approach.

Research limitations/implications

The penalty approach is applied to some different boundaries: partial slip and partial penetration with no/full slip/penetration as limiting cases; free surface; space‐ and time‐varying boundary conditions which allow progressive contact over time. Application is made to curved and inclined boundaries. Sensitivity of flow to penalty parameters is an avenue for continued research, as is application of the penalty approach for non‐Newtonian flows.

Originality/value

This is the first work to show the relation between penalty formulation of boundary conditions and physical boundary conditions. It provides a method that overcomes past difficulties in implementing partial slip on boundaries of general shape, and which handles progressive contact. It also provides useful benchmark problems for future studies.

Keywords

Citation

Stokes, Y. and Carey, G. (2011), "On generalised penalty approaches for slip, free surface and related boundary conditions in viscous flow simulation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 6, pp. 668-702. https://doi.org/10.1108/09615531111148455

Publisher

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Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited