Tham khảo tài liệu 'applied computational fluid dynamics techniques - wiley episode 2 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | INTERPOLATION 267 Table . Particle-mesh interpolation timings ON F OFF V ON F Particle-tracing time s MFLOP-rate recorded Total running time s Timings s particle step At the beginning the particles were placed uniformly across the mesh following a square lattice of nppdixnppdi particles. Figure shows a typical sequence of 20 steps for npart 5x5 particles. In an effort to obtain an accurate timing the following set of parameters was used - npart 10 000 this large set of particles minimizes the overhead associated with subroutine calls - ntime 5 0 0 this large number of timesteps minimizes the start-up overheads. The particles were moved a distance of dista every timestep. On the mesh used at most six elements had to be tested for each particle to locate the new host element. However in most cases only five elements required testing. The average number of remaining particles after each search pass . those that have not yet found their host elements is shown in the histogram given by Figure . To obtain timings two runs were performed on a Cray-XMP with and without automatic vectorization. The Cray-XMP allowed the required gather scatter operations to be run in hardware. The timings obtained are listed in Table below. The results demonstrate a 14-fold speedup when using the automatic vectorization. Factors like these enable new dimensions of reality in simulations making it possible to study new phenomena previously thought untractable. 14 ADAPTIVE MESH REFINEMENT The development of self-adaptive mesh refinement techniques in computational fluid dynamics CFD computational structural dynamics CSD computational electromagnetics CEM and other fields of computational mechanics is motivated by a number of factors. a With mesh adaptation the numerical solution to a specific problem given the basic accuracy of the solver and the desired accuracy should be achieved with the fewest degrees of freedom. This
