Nobuatsu Tanaka

Development of a highly accurate interpolation method for mesh-free flow simulations I. Integration of gridless, particle and CIP methods

A simple, efficient, flexible and accurate interpolation method, CIVA, is introduced for use with mesh-free methods for flow simulations. The method enables mesh-free cubic interpolation with the local co-ordinate system, such as volume and area co-ordinates, by utilizing the concept of the CIP scheme and allows the development of new highly accurate mesh-free methods. The mesh-free methods integrate the gridless, particle and CIP methods since they have flexibility in the treatment of moving calculation points. For achieving high accuracy with the CIVA method, it is also important to correctly evaluate particle movement. The improvement of the evaluating algorithm is another objective of this study. The validity of the algorithms is confirmed by applying them to the convection and convection-diffusion problems. Since the CIVA-based mesh-free methods enable flexible, efficient and accurate fluid simulation, they make it possible to perform highly accurate simulations of many kinds of problems that involve complicated geometries and phenomena

Incomplete Discrete Wavelet Transform and Its Application to a Poisson Equation Solver

Recently there have been many developments and new applications of mathematical techniques for describing complex functions and analyzing empirical continuous data derived from many different types of signals. The wavelet theory would be the most important and rapidly developing among these techniques. Wavelets have provided a new method for decomposing a function or signal, just like a Fourier expansion. Several articles on wavelets exhibit the wide variety of applications of wavelet analysis and present many of the key developments of the theory. Daubechies[1] proposed families of compactly supported wavelets with certain degrees of smoothness which are constructed by using multiresolution analysis[2].