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

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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.