An embedding finite element method for viscous incompressible flows with complex immersed boundaries on Cartesian grids

• Published in: Engineering computations 2014-01, Vol.31 (4), p.656-680
• Main Authors: Lo, D.C., Hsieh, Chih-Min, Young, D.L.
• Format: Article
• Language: English
• Subjects: Accuracy; Aerospace engineering; Aircraft; Approximation; Boundaries; Boundary conditions; Computer simulation; Cylinders; Engineering; Finite element analysis; Finite element method; Fluids; Mathematical analysis; Mathematical models; Methods; Navier-Stokes equations; Reynolds number; Studies; Velocity
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-04-2012-0090

Purpose – The main advantage of the proposed method is that the computations can be performed on a Cartesian grid with complex immersed boundaries (IBs). The purpose of this paper is to device a numerical scheme based on an embedding finite element method for the solution of two-dimensional (2D) Navier-Stokes equations. Design/methodology/approach – Geometries featuring the stationary solid obstacles in the flow are embedded in the Cartesian grid with special discretizations near the embedded boundary to ensure the accuracy of the solution in the cut cells. To comprehend the complexities of the viscous flows with IBs, the paper adopts a compact interpolation scheme near the IBs that allows to satisfy the second-order accuracy and the conservation property of the solver. The interpolation scheme is designed by virtue of the shape function in the finite element scheme. Findings – Three numerical examples are selected to demonstrate the accuracy and flexibility of the proposed methodology. Simulation of flow past a circular cylinder for a range of Re=20-200 shows excellent agreements with other results using different numerical schemes. Flows around a pair of tandem cylinders and several bodies are particularly investigated. The paper simulates the time-based variation of the flow phenomena for uniform flow past a pair of cylinders with various streamwise gaps between two cylinders. The results in terms of drag coefficient and Strouhal number show excellent agreements with the results available in the literature. Originality/value – Details of the flow characteristics, such as velocity distribution, pressure and vorticity fields are presented. It is concluded the combined embedding boundary method and FE discretizations are robust and accurate for solving 2D fluid flows with complex IBs.