  A high-performance gas kinetic solver using multi-level parallelization is
developed to enable pore-scale simulations of rarefied flows in porous media.
The Boltzmann model equation is solved by the discrete velocity method with an
iterative scheme. The multi-level MPI/OpenMP parallelization is implemented
with the aim to efficiently utilise the computational resources to allow direct
simulation of rarefied gas flows in porous media based on digital rock images
for the first time. The multi-level parallel approach is analyzed in details
confirming its better performance than the commonly-used MPI processing alone
for an iterative scheme. With high communication efficiency and appropriate
load balancing among CPU processes, parallel efficiency of 94% is achieved for
1536 cores in the 2D simulations, and 81% for 12288 cores in the 3D
simulations. While decomposition in the spatial space does not affect the
simulation results, one additional benefit of this approach is that the number
of subdomains can be kept minimal to avoid deterioration of the convergence
rate of the iteration process. This multi-level parallel approach can be
readily extended to solve other Boltzmann model equations.
