Implementation of slip boundary conditions in the finite volume method: new techniques

• Published in: International journal for numerical methods in fluids 2013-07, Vol.72 (7), p.724-747
• Main Authors: Ferrás, L.L., Nóbrega, J.M., Pinho, F.T.
• Format: Article
• Language: English
• Subjects: Boundary conditions; Computational fluid dynamics; Finite element method; finite volume method; Fluid flow; implicit method; Law; Mathematical models; Nonlinearity; Slip; slip boundary condition
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.3765

SUMMARY Two different techniques for the implementation of the linear and nonlinear slip boundary conditions into a finite volume method based numerical code are presented. For the linear Navier slip boundary condition, an implicit implementation in the system of equations is carried out for which there is no need for any relaxation, especially when handling high slip coefficients. For three different nonlinear slip boundary conditions, two different methods are devised, one based on solving a transcendental equation for the boundary and the other on the linearization of the slip law. For assessment purposes, comparison is made between these new methods and the usual iterative process. With these new methods, the convergence difficulties, typical of the iterative procedure, are eliminated, and for some of the test cases, the convergence rate even increased with the slip velocity. The details of these implementations are given first for a simple geometry using orthogonal meshes and Cartesian coordinates followed by their generalization to non‐Cartesian coordinates and nonorthogonal meshes. The developed code was tested in the benchmark slip‐stick and 4:1 contraction flows, evidencing the robustness of the proposed procedures. Copyright © 2013 John Wiley & Sons, Ltd. New strategies for the implementation of slip boundary conditions in the finite volume method are presented, comprising an implicit scheme for the linear slip model and semi‐implicit schemes for non‐linear slip laws in orthogonal and non‐orthogonal meshes. The figure shows the number of iterations required to achieve convergence when solving the Poiseuille flow between parallel plates problem using the following schemes: implicit (SSI), explicit (SSE), semi‐implicit transcendent (SSSIT) and semi‐implicit SSSI (for the linear Navier slip law).