На 03 декември 2012 г. в Заседателната зала на ХТМУ се проведе научен семинар в областта на крайно-диференчните схеми.
Беше изнесена лекция на тема "Basic Concept оf а Spectral Finite Difference Scheme"
от Prof. Yoshihiro Mochimaru, Tokyo Iinstitute of Technology, Japan
Outline of the lecture:
Basic idea on spectral finite difference schemes for solutions of partial differential equations is presented, compatible with conformal mapping. In the lecture, concrete examples for application of a spectral finite difference scheme are given in a twodimensional case, although usage of a spectral finite difference scheme is not restricted to such a case. First of all twodimensional natural laminar convection of substantially incompressible Newtonian fluid is considered.
1) Analytical construction of a boundaryfitted coordinate system even for a multiplyconnected domain to reduce to a boundaryvalue problem.
2) Introduction of a conformal mapping system univalent in the domain (except zero measure if possible), which is not uniquely determined as long as boundary
configuration is specified a priori.
3) Exact spectral decomposition based on complete series to the governing partial differential equations, supplemented with multiplyconnectedness if necessary.
4) Application is not restricted to heat and fluid flow problems. It can be applied to diffusion problems and others.