非结构网格上可压缩Euler方程的并行算法

Parallel Algorithm for Compressible Euler Equations on Unstructured Grids

为了提高双曲守恒律的求解效率,提出了在分布式环境下基于多级图分区方法的并行求解策略。通过多级图分区方法划分非结构网格,使得多块区域网格独立保存。内边界构造虚拟单元进行数据传递,最大限度减少通信开销,并加入当地时间步长以及隐式时间离散技术进一步提高计算效率,最终形成总体耦合流场解。在集群系统上,计算了NACA0012翼型和DLR-F6翼身组合体无黏跨音速流动,10台处理机并行效率保持在70%以上,随着计算网格量的增加,并行效率和加速比进一步提高,验证了该方法的可行性和高效性。数值结果表明,该算法适合MIMD分布式环境下进行粗粒度科学计算。

Efficient parallel algorithm based on multilevel k-way partitioning method on distribut- ed-memory multi-computers was proposed for solving conservation laws on unstructured grids in order to accelerate the efficiency. Multilevel k-way partitioning algorithm was employed to handle meshes properly and save each partition mesh individually. The data of inner boundary was transferred through the virtual units, which makes each processor maintain load balancing. The implicit scheme and local time stepping techniques were used to accelerate the convergence of the solution of unsteady Euler equations to steady state. Numerical experiment performed for inviscid transonic flows around NA- CA0012 airfoil and DLR-F6 geometry （wing-body-pylon-nacelle） indicated that the proposed parallel algorithm have the advantages of high acceleration and efficiency. With the increase of the meshes, the speedup and accelerator further improve and the efficiency of 10 processors which remains above 70%. The numerical solutions indicate that the presented algorithm is suitable for large-grained science com- puting on MIMD model.