A novel approach to eliminate error induced by cell to node projections. (12th August 2015)

• Record Type: Journal Article
• Authors: Li, Peichao; Zhang, Lingbo; Li, Peilun
• Is Part Of: International journal for numerical and analytical methods in geomechanics. Volume 40:Number 5(2016)
• Page Start: 676
• Page End: 685
• Publication Date: 2015-08-12
• Subjects: FSI in porous media -- cell to node projection scheme -- error induced by projection -- error formula -- error control factor; Soil mechanics -- Mathematics -- Periodicals; Rock mechanics -- Mathematics -- Periodicals; 624.1510151
• DOI: 10.1002/nag.2422
• Languages: English
• ISSNs: 0363-9061

Abstract

Summary: In engineering practices, different numerical methods for fluid flow simulation and solid deformation/stress simulation are adopted to model fluid–structure interaction problems in porous media. Cell‐centered finite volume method is widely used in fluid flow simulation, while the solid deformation/stress simulation is usually accomplished by using the Galerkin vertex‐centered finite element method, which leads to the incompatibility between cell variables with nodal variables. Therefore, the data transfer between cell variables and nodal variables is inevitable. Consequently, this kind of transfer will lead to extra artificial error. Hence, the major concern is how to minimize the error due to cell to node projections. In this paper, a problem of pore pressure diffusion within a one‐dimensional heterogeneous porous medium is investigated. We present a new projection scheme and corresponding error formula, where the error control factor is introduced. The new projection scheme is based on piecewise linear interpolations. Results demonstrate that if the error control factor is chosen properly, the error due to the projection from cell to node can be controlled effectively, and the most desired zero error can be achieved. Finally, we analyze some practical cases in consideration of permeability contrast and mesh uniformity. Copyright © 2015 John Wiley & Sons, Ltd.