Research on a highly accurate parallel numerical methods for fluid equations with portability

本研究的目的是在计算科学的并行计算环境的发展计算流体动力学的研究。本文研究了两个目标：1）高精度、高分辨率的流体现象数值计算方法; 2）基于JAVA语言的可移植性强的计算环境。主要结果如下：1）针对不可压缩和可压缩流体流动，提出了三种新的组合紧致差分格式。这些格式数值稳定，精度高，分辨率高.我们还研究了组合紧致差分格式的数值稳定性和高精度边界条件。将这些格式的数值结果与传统数值方法在四倍网格系统下的数值结果进行了比较。2）利用Java语言开发了两个具有容错能力的并行数值模拟系统。在第一个系统中，我们采用了一个主-工人模型，以解决这个问题，通常的编程是脆弱的计算系统的任何类型的故障。我们已经验证了，只要至少有一个工作进程，并且动态分配进程，系统的完整性就能很好地保持。第二计算系统应用于P2P类型模型的网络，并且能够在该系统中动态地添加和移除计算资源。我们实现了这个计算系统在PC集群，并评估该系统的性能。该系统比第一个系统更健壮、更灵活，但计算速度较慢，这些新的数值方法和数值环境将使我们能够方便灵活地在多台PC机上高精度、高分辨率地模拟各种流动现象。

The purpose of this research in Computational Science is the development of the parallel computational environments for computational fluid dynamic research. Two objects have been investigated : 1)Numerical method of fluid phenomena with high accuracy and high resolution, 2)Robust computational environments using a JAVA language with portability. The following results are obtained.1)New three numerical schemes using combined compact difference schemes are proposed for incompressible and compressible fluid flows. These schemes are numerically stable and have high accuracy and resolution. We also investigate the numerically stable and high accurate boundary conditions for the combined compact difference schemes. The numerical results using these schemes are compared with those of the traditional numerical methods with a four times finer grid system.2)We developed two robust and flexible parallel systems for numerical simulations using the Java language which has fault tolerance for Grid Computing. In the first system, we adopt a master-worker model in order to settle the issue that usual programming is vulnerable to any kind of failure of the computing system. We have verified that the system integrity is nicely held as long as there is at least one worker process and that dynamic allocation of processes. The second computing system is applied to a network of a P2P type model and it is able to add and remove computing resources dynamically in this system. We implement this computing system in PC clusters and evaluate this system performance. This system is more robust and flexible than the first system but its computational speed is slow.These new numerical method and numerical environment will make it easy and flexible to simulate the accurate various flow phenomena with high accuracy and high resolution using a number of PCs.