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

计算科学的这项研究的目的是开发用于计算流体力学研究的并行计算环境。研究了两个目标：1)高精度、高分辨率的流体现象数值方法；2)使用具有可移植性的Java语言实现健壮的计算环境。1)针对不可压缩流体流动和可压缩流体流动，提出了三种新的紧致差分格式。这些格式数值稳定，具有较高的精度和分辨率。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。2)利用具有网格计算容错功能的Java语言，开发了两个健壮、灵活的数值模拟并行系统。在第一个系统中，我们采用了主-从模型，以解决通常的编程容易受到计算系统任何类型故障的影响的问题。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，系统的完整性就能得到很好的保持。第二计算系统应用于P2P模式的网络，能够在该系统中动态地添加和移除计算资源。我们在PC集群上实现了该计算系统，并对该系统进行了性能评估。这种新的数值方法和数值环境使得在多台PC机上对各种流动现象进行高精度、高分辨率的数值模拟变得容易和灵活。

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.