Multi-Layer Cartesian Cell Registration for Efficient DSMC Particle Search on a Strongly Non-Uniform Body-Fitted Mesh

A Multi-Layer extension of Cartesian Cell Registration (CCR) is proposed for particle-location search in Direct Simulation Monte Carlo (DSMC) on strongly non-uniform body-fitted meshes. The method uses radially nested background Cartesian grids with different cell widths so that the number of target cells registered to each Cartesian cell remains of order unity across the domain. It is assessed for two-dimensional rarefied flow around a circular cylinder using a Bird-derived DSMC solver with PMU-based profiling of the particle-motion stage. In the present implementation, the final containment judgment is performed by a conventional point-in-cell test so that the comparison isolates the search cost. The results show that the practical optimum is obtained at an intermediate average registration count of about five target cells per Cartesian cell. Relative to brute-force search, this setting reduces the average candidate count, REG1 cycles per call, and total measured cycles per molecule by factors of 2960, 44.5, and 23.6, respectively. Statistical analysis further shows that about 27% of traced particle moves cross at least one target-cell boundary, demonstrating the practical advantage of CCR when the single-cell-per-move assumption is not always satisfied.