Grid-free octree approach for modeling heat transfer to complex geometries

The grid-free octree direct simulation Monte-Carlo algorithm has been explored to simulate flows through and heat transfer to highly irregular geometries for finite Knudsen numbers. The approach was extended to accurately compute the volume of irregular octree clusters as well as a line-of-sight test before performing collisions in octree clusters that are intersected by a solid boundary. The modified grid-free octree direct simulation Monte-Carlo algorithm was tested for the classic Fourier and micro-Poiseuille flows. A single sphere as well as an aggregate of spheres were modeled in a 500Kheat bath and supersonic flow. For the heat bath case, it was observed that a two-level Cartesian grid direct simulation Monte-Carlo code was able to achieve the same heat flux to a single sphere as the octree approach if 10 times more computational particles were used. Furthermore, even with increased computational load, the two-level Cartesian approach encountered a difference of 15% from the octree calculation for heat flux for interior spheres due to shielding by outer spheres. It was found that, for supersonic flows surrounding a single sphere and an aggregate, the octree approach was able to resolve the detached bow shock as well as the wake region, and in the aggregate case, the spatial resolution was sufficient to capture distinct multiple shocks in terms of temperature jump and pressure contours. Computational efficiency in terms of central processing unit-graphical processing unit computing is also discussed.