ashapecompressiblejcp

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A sharp interface immersed boundary method for compressible viscous flows R. Ghias, R. Mittal * , H. Dong Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, DC 20052, United States Received 6 February 2006; received in revised form 15 December 2006; accepted 15 December 2006 Available online 23 December 2006 Abstract An immersed boundary method for computing viscous, subsonic compressible flows with complex shaped stationary immersed boundaries is presented. The method employs a ghost-cell technique for imposing the boundary conditions on the immersed boundaries. The current approach leads to a sharp representation of the immersed boundaries, a property that is especially useful for flow simulations at high Reynolds numbers. Another unique feature of the method is that it can be applied on Cartesian as well as generalized body non-conformal curvilinear meshes. A mixed second-order central dif- ference-QUICK scheme is used which allows a high degree of control over the numerical damping. A bilinear interpolation scheme used in conjunction with the ghost-cell approach results in second-order global as well as local spatial accuracy. The solver is parallelized for distributed memory platforms using domain decomposition and message passing interface (MPI) and salient features of the parallel algorithm are presented. The accuracy, fidelity and efficiency of the solver are examined by simulating flow past circular cylinders and airfoils and comparing against experimental data and other estab- lished results. Finally, we present results from a simulation of wing-tip flow at a relatively high Reynolds number in order to demonstrate the ability of the solver to model complex, non-canonical three-dimensional flows. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Computational fluid dynamics; Immersed boundary method; Ghost-cell; Non-conformal grid 1. Introduction The conventional structured grid approach to simulating flows with complex immersed boundaries is to dis- cretize the governing equations on a curvilinear grid that conforms to the boundaries. Since the boundary itself becomes a grid line, the imposition of boundary conditions is greatly simplified and the solver can be easily designed to maintain adequate accuracy and conservation properties. However, depending on the geo- metrical complexity of the immersed boundary, grid generation and grid quality can be major issues and one has to resort to multi-block or other such approaches in order to handle anything but the simplest geometries. For complex bounda rie s, uns tru ctur ed grid meth ods offer gre ater flexi bil ity and are bei ng widely use d. 0021-9991/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2006.12.007 * Corresponding author. Tel.: +1 202 994 9394. E-mail address: [email protected] (R. Mittal). Journal of Computational Physics 225 (2007) 528–553 www.elsevier.com/locate/jcp

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