Table of Contents
Journal of Computational Engineering
Volume 2014 (2014), Article ID 768538, 11 pages
Research Article

Modal Spectral Element Solutions to Incompressible Flows over Particles of Complex Shape

1Mathematics & Statistics and Mechanical Engineering, Louisiana Tech University, Ruston, LA 71272, USA
2Department of Hydraulic Engineering, School of Civil Engineering, Tongji University, Shanghai 200092, China

Received 22 February 2014; Accepted 6 April 2014; Published 30 April 2014

Academic Editor: Quan Yuan

Copyright © 2014 Don Liu and Yonglai Zheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper develops the virtual identity particles (VIP) model to simulate two-phase flows involving complex-shaped particles. VIP assimilates the high efficiency of the Eulerian method and the convenience of the Lagrangian approach in tracking particles. It uses one fixed Eulerian mesh to compute the fluid field and the Lagrangian description to handle constitutive properties of particles. The interaction between the fluid and complex particles is characterized with source terms in the fluid momentum equations, while the same source terms are computed iteratively from the particulate Lagrangian equations. The advantage of VIP is its economy in modeling a two-phase flow problem almost at the cost of solving only the fluid phase with added source terms. This high efficiency in computational cost makes VIP viable for simulating particulate flows with numerous particles. Owing to the spectral convergence and high resolvability of the modal spectral element method, VIP provides acceptable resolution comparable to DNS but at much reduced computational cost. Simulation results indicate that VIP is promising for investigating flows with complex-shaped particles, especially abundant complex particles.