The General Quadrant Meshing Approach for Constructive Solid Geometry Based Method of Characteristics

Abstract The constructive solid geometry (CSG) method is widespread in codes based on Monte Carlo and the method of characteristics (MOC). Unlike just modelling the material regions in the Monte Carlo method, the MOC needs to split the material regions into small flat source region (FSR) meshes. The main obstacle standing ahead in using CSG methods for geometric modeling of MOC is the meshing of complex regions. Unstructured triangular mesh is introduced in MOC codes such as DIAMOND and ThorMOC to mesh on complex geometry. The geometry modeling ability is indeed greatly enhanced by using unstructured triangular mesh. However, the unstructured triangular mesh requires a small amount of initial overhead to generate and refine the mesh. Furthermore, small regions, like fuel rod cladding in PWR, need a lot of triangle meshes, which lead to very small track spacing and huge memory requirements. As a result, a general quadrant meshing (GQM) technique for complex geometry modeling with CSG is proposed in this paper and has been implemented in the 2D MOC. The GQM bounds the target CSG grid with a rectangle. By setting number of grids on the horizontal and vertical edge, the rectangle is then converted to a quadrant mesh. The grid that is in the CSG grid will be added as the sub-cells. The grid that is out of the CSG grid will be ignored. And the grid that crossed by the CSG grid boundaries will be added as the sub-cells after merging all the CSG grid surfaces. The volume of grid that crossed by the CSG grid boundaries is recomputed by the Monte Carlo method or the integration method. The point coordinates are random generated in the Monte Carlo method and the coordinates are the center of each quadrant mesh in the integration method. If the number of points is greater than 106 in the bounding rectangular cell, the volume relative error is less than 10−2 under most circumstances. A performance comparison between triangular unstructured meshes and the GQM is presented in this paper. The results of CANDU-6 bundle problem demonstrates the superiority of the CSG quadrant meshing method with respect to the unstructured triangular mesh. In the CANDU-6 bundle problem, the scalar flux and keff of GQM are nearly the same as triangular unstructured mesh while the grid number is only slightly more than half of the triangular unstructured mesh. To verify the accuracy of the 2D MOC code developed in this paper, many other transport benchmarks with different geometries, including BWR and PWR lattice, etc. were performed. Results of all the tested problems show good agreement with the references.