A novel discretization method for the N-S equations on three-dimensional Cartesian cut cell

A novel three-dimensional Cartesian cut cell algorithm, referred to as 6+N, is proposed to describe and treat arbitrary three-dimensional Kitta Cube. This method can avoid the enumeration for millions of cutting patterns and implement the discretization and solution of the N-S equations in a unified form. The present method is applied to simulate natural convection heat transfer in an annular tunnel between two concentric or eccentric spheres. The numerical results show that Kitta Cube can express curve surfaces accurately with an error of less than 1.0%. The accuracy of solutions obtained by the present method is approximately equivalent to that by the body-fitted method. In addition, higher overall heat transfer coefficients can be achieved by lowering the position of the inner sphere for eccentric arrangement.