DEVELOPMENT OF A VIRTUAL NUMERICAL LABORATORY FOR EARTH-PLANETARY FLUID DYNAMICS USING SPECTRAL METHODS

本研究的目的是在因特网上建立一个地球行星流体的虚拟“数值实验室”。在发展必要的谱方法方面，发展了一种新的求解圆盘上浅水波方程的谱方法，其详细内容已作为两篇原创论文发表。该方法采用雅可比多项式作为展开基，避免了采用极坐标时常出现的原点奇异性。该方法的新奇在于直接将向量场展开，另外，还发展了一维/二维无限域的谱方法，目前正在准备中。利用该技术，对浅水系统中不稳定射流的重力波辐射进行了数值实验。重力波的参数依赖性进行了检查，它是作为提交的论文作出贡献。开发的数字库作为http://www.gfd-dennou.org/arch/ispack/ispack-0.62beta.tar.gz免费分发。此外，还根据数值图书馆的开发经验，出版了日本第一本谱方法教科书。为了提供虚拟实验室环境，新启动了一个坚固的Web服务器，该服务器不仅保存了一系列用于地球行星流体计算的谱模型的源代码和解释，而且还保存了一个典型练习的执行结果。这些内容通过http://www.gfd-dennou.org/arch/spmodel/免费发布。

The research was accomplished aiming to construct a virtual "numerical laboratory" of earth planetary fluid in the Internet.As for the development of necessary spectral methods, a new spectral method was developed for shallow water equations on a disk, the details of which are published as two original papers. This method uses Jacobi polynomials as a basis of expansion to avoid the singularity at the origin which often appears when the polar coordinate is adopted. The novelty of the method is in expanding vector fields directly.In addition, new spectral methods for 1d/2d infinite domains are developed, and the paper is being prepared now. By using this technique, numerical experiments of gravity wave radiation from an unstable jet in a shallow water system are conducted. The parameter dependency of the gravity waves are examined, and it is contributing as a submitted paper. The developed numerical library is distributed freely as http://www.gfd-dennou.org/arch/ispack/ispack-0.62beta.tar.gz. Furthermore, the first textbook for spectral methods in Japanese is published based on the experiences in the development of the numerical library.To provide the virtual laboratory environment, a firm web server is newly started up, which maintains not only the source code of a series of developed spectral models for the earth planetary fluid calculation and the explanation, but also the execution result of a typical exercise. The contents are distributed freely as http://www.gfd-dennou.org/arch/spmodel/.