A clipping algorithm on non-conformal interface for heat conduction analysis

In numerical analysis of heat transfer including complicated computational domains or geometries, the domains are divided into several simple domains, and it is possible to generate cells in the simple domains easily. However, for the sake of the isolation of the domains, the methods lead the vertex mismatch between the divided regions, and become non-conformal. Because of the non-conformal meshes, it is difficult to calculate fluxes through the interface. Therefore, a computational treatment for the non-conformal mesh is required to obtain geometrical information between neighboring cells. A clipping method to find the geometrical information are developed, and applied to thermal conduction problems. The clipping method implemented in this study is advantageous in using simple vector operations only to obtain the geometrical information on the non-conformal interface. To test the accuracy of the clipping method, twelve cases with different grid configurations are presented. They show that the method has a high degree of accuracy for calculating the clipped areas. Furthermore, to validate the scheme, the heat conduction problem is performed. And then, the numerical result agrees well with the exact solution. Additionally, we apply the scheme to the fourth case in the ISO 10211 that includes two materials with different aspect ratios. In the vicinity of the interface, the high temperature gradients are presented because of the different thermal conduction coefficients. Therefore, it shows that the present methods can treat the non-conformal meshes with the different neighboring cell size properly.