دانلود رایگان مقاله اجرای موازی پویایی شوک هندسی برای موج همگرای شوک دو بعدی

Abstract

Geometrical shock dynamics (GSD) theory is an appealing method to predict the shock motion in the sense that it is more computationally efficient than solving the traditional Euler equations, especially for converging shock waves. However, to solve and optimize large scale configurations, the main bottleneck is the computational cost. Among the existing numerical GSD schemes, there is only one that has been implemented on parallel computers, with the purpose to analyze detonation waves. To extend the computational advantage of the GSD theory to more general applications such as converging shock waves, a numerical implementation using a spatial decomposition method has been coupled with a front tracking approach on parallel computers. In addition, an efficient tridiagonal system solver for massively parallel computers has been applied to resolve the most expensive function in this implementation, resulting in an efficiency of 0.93 while using 32 HPCC cores. Moreover, symmetric boundary conditions have been developed to further reduce the computational cost, achieving a speedup of 19.26 for a 12-sided polygonal converging shock.

4. Conclusions

In this study, a spatial decomposition method to implement the GSD simulation on parallel computers was adopted. At first, performance profiling was conducted to analyze computational hot-spot in the serial scheme. Two schemes were designed to parallelize the simulation, in which MPI and OpenMP were employed. An efficient tridiagonal solver [17] based on the SPIKE algorithm [20,21] was also incorporated into the parallel implementation to handle the most computationally expensive function. Performance analysis and comparison between the two schemes were investigated. The hybrid scheme shows its advantage of implementation ease and the running result demonstrates its speedup, 9.7, on 16 HPCC node-processors. On the other hand, the MPI scheme leads to an improved performance in efficiency and scalability. The strong-scaling experiment proves a high efficiency of 0.93 using 32 HPCC cores, while the isogranular-scaling experiment shows that the efficiency holds up to 0.83 using 64 HPCC cores. To further improve the speedup for symmetric converging shock simulations, symmetric boundary conditions were developed to reduce the problem size considerably. Results have shown that for a dodecagonal converging shock front, a speedup of up to 19.26 can be achieved. Although this study only focuses on converging shock configurations, the parallel schemes can be easily extended to solve more generalized shock setups by changing the boundary conditions. In the future, parallelization on three dimensional GSD model will be investigated.