The Multi-core Optimization of the Unbalanced Calculation in the Clean Numerical Simulation of Rayleigh-Bénard Turbulence

The so-called clean numerical simulation (CNS) is used to simulate the Rayleigh-Bénard (RB) convection system. Compared with direct numerical simulation (DNS), the accuracy and reliability of investigating turbulent flows improve largely. Although CNS can well control the numerical noises, the cost of calculation is more expensive. In order to simulate the system in a reasonable period, the calculation schemes of CNS require redesign. In this paper, aiming at the CNS of the two-dimension RB system, we first propose the notions of equal difference matrix and balance point set which are crucial to model the unbalanced calculation of the system under multi-core platform. Then, according to the notions, we present algorithms to optimize the unbalanced calculation. We prove our algorithm is optimal when the core number is the power of 2 and our algorithm approaches the optimal when the core number is not the power of 2. Finally, we compare the results of our optimized algorithms with others to demonstrate the effectiveness of our optimization.