INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids (2011) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/fld.2678 A three-dimensional Cartesian cut cell method for incompressible viscous flow with irregular domains X. L. Luo 1 , Z. L. Gu 1, * ,† , K. B. Lei 2 , S. Wang 2 and K. Kase 2 1 School of Human Settlement and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, China 2 VCAD Modeling Team, RIKEN Institute, Japan SUMMARY A three-dimensional Cartesion cut cell method is presented for the simulations of incompressible viscous flows with irregular domains. A new model (referred to as ‘6+N’ model) is proposed to describe arbitrarily shaped cut cells and treat all the cells as polyhedrons with 6+N faces. The finite volume discretization of the Navier–Stokes equation is then implemented by using the ‘6+N’ model to separate the surface flux integrals into two parts, that is, the fluxes through the basic face of the hexahedron and those through the cutting surfaces. The previously proposed Kitta Cube algorithm and volume computer-aided design platform .J. Comput . Aided. Des . 2005; 37(4): 1509–1520. Doi:10.1016/j.cad.2005.03.006) are adopted to generate cut cells and provide shape data and physical attributes for the numerical analysis. A modified SIMPLE-based smoothing pressure correction scheme is applied to suppress checkerboard pressure oscil- lations caused by the collocated arrangement of velocities and pressure. The calculation accuracy of the numerical method expressed by L 1 and L 1 norm errors is first demonstrated by the simulation of a pipe flow. Then its feasibility, efficiency, and potential in engineering applications are verified by applying it to solve natural convections between concentric spheres and between eccentric spheres. The heat transfer pat- terns in eccentric spheres are also obtained by using the numerical method. Copyright © 2011 John Wiley & Sons, Ltd. Received 8 October 2010; Revised 8 July 2011; Accepted 12 August 2011 KEY WORDS: finite volume method; Kitta Cube; volume CAD; Cartesian cut cell; ‘6 + N’ model; smoothing pressure correction scheme; natural convection 1. INTRODUCTION The CFD technique has become an indispensable tool for numerical analysis and industrial design. The geometry of interest tends to be extremely complex in many cases. The increasing demands on various personalized elements make the geometry even more complex and diverse. The gener- ation of a computational mesh is one of the first tasks to be faced in CFD. Although various mesh generation methods are available (see [1] for a detailed introduction), generating a suitable mesh for a complex geometry remains a time-consuming task and usually requires much more time than simulating a fluid flow. Automatic mesh generation methods and easy-to-use mesh generation tools are strongly desired to reduce the effort in mesh generation. The Cartesian cut cell method might offer the best hope for achieving automatic grid genera- tion for a complex geometry in practical applications. Conceptually, this approach is quite simple. Briefly, solid bodies are cut out of a background Cartesian mesh and their boundaries are repre- sented by different types of cut cells. The Cartesian cut cell method has been gaining popularity in the simulations of viscous and inviscid flows because of its automation and ability to decompose *Correspondence to: Z. L. Gu, School of Human Settlement and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, China. † E-mail: guzhaoln@mail.xjtu.edu.cn Copyright © 2011 John Wiley & Sons, Ltd.