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Mathematical Problems in Engineering
Volume 2015, Article ID 438086, 17 pages
Research Article

A Simple Immersed Boundary Method for Compressible Flow Simulation around a Stationary and Moving Sphere

1Tokai University, 4-1-1 Kitakaname, Hiratsuka, Kanagawa 259-1292, Japan
2ISAS/JAXA, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan

Received 19 June 2015; Accepted 6 September 2015

Academic Editor: Yihua Lan

Copyright © 2015 Yusuke Mizuno et al. 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 study is devoted to investigating a flow around a stationary or moving sphere by using direct numerical simulation with immersed boundary method (IBM) for the three-dimensional compressible Navier-Stokes equations. A hybrid scheme developed to solve both shocks and turbulent flows is employed to solve the flow around a sphere in the equally spaced Cartesian mesh. Drag coefficients of the spheres are compared with reliable values obtained from highly accurate boundary-fitted coordinate (BFC) flow solver to clarify the applicability of the present method. As a result, good agreement was obtained between the present results and those from the BFC flow solver. Moreover, the effectiveness of the hybrid scheme was demonstrated to capture the wake structure of a sphere. Both advantages and disadvantages of the simple IBM were investigated in detail.