Running a large-scale Spiking Neural Network （SNN） on a distributed computing platform is one of the basic means to improve the level of brain-like computing intelligence. The difficulty lies in how to deploy the SNN to the corresponding number of computing nodes in order to make the overall system run with the best energy efficiency. To solve this problem， on the basis of NEural Simulation Tool-based （NEST-based） Workload Automatic Mapper for SNN （SWAM） proposed by others before， a workload automatic mapper for SNN， named SWAM2， based on precise communication modeling was proposed. In SWAM2， based on the NEST simulator， the communication part of the SNN workload was further accurately modeled； the quantization method of the parameters in the workload model was improved； the maximum network scale prediction method was designed. Experimental results on typical cases of SNN show that， the average prediction errors of SWAM2 were reduced by about 12.62 and 5.15 percentage points respectively compared with those of SWAM in workload communication and computing time prediction. When predicting the optimal mapping of the workload， the average accuracy of SWAM2 reached 97.55%， which was 13.13 percentage points higher than that of SWAM. SWAM2 avoids the process of manual trial and error by automatically predicting the optimal deployment/mapping of SNN workload on computing platform.