An X‐FEM‐based numerical–asymptotic expansion for simulating a Stokes flow near a sharp corner. (29th August 2014) - Foucard, Louis C.
Summary A numerical technique that is based on the integration of the asymptotic solution in the numerical framework for computing the local singular behavior of Stokes flow near a sharp corner is presented. Moffat's asymptotic solution is used, and special enriched shape functions are developed and integrated in the extended finite element method (X‐FEM) framework to solve the Navier–Stokes equations. The no‐slip boundary condition on the walls of the corner is enforced via the use of Lagrange multipliers. Flows around corners with different angles are simulated, and the results are compared with both those of the known analytic solution and the X‐FEM with no special enrichment near the corner. The results of the present technique are shown to greatly reduce the error made in computing the pressure and velocity fields near a corner tip without the need for mesh refinement near the corner. The method is then applied to the estimation of the permeability of a network of fibers, where it is shown that the local small‐scale pressure singularities have a large impact on the large‐scale network permeability. Copyright © 2014 John Wiley & Sons, Ltd.