Mathematical analysis of water and air flow in the life and its computer simulation.

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The purpose of the research project is to investigate mathematical aspects of the flow of water and air closely connected to our life, and develop a computer simulation program implemented on PC.The objectives are set as fol lows :1.The finite element method is used for numerical solution of flow equations in order to cope with the complex geometry of the flow domian in question. The governing equations are discretized by using the fractional step method for incompressible viscous fluid flow and using the Taylor-Galerkin's method for flow in shallow waters. The unknowns are interpolated by using the linear triangular element.2.An integrated package of computer simulation with pre- and post-processors is developed concerning the flow of water and air in the life for handy and practical use to assess the flow environment. The computer program is revised on the easy-to-use base reflected from the claims served by tentative users.3.The flows are presented as solutions of initial-boundary value problems of partial differential equations. Domain in the flow simulation often has a so-called open boundaries, which are formed by cutting artificially the real flow domain. The boundary condition on the open boundaries are not a priori given. Suitable boundary conditions are crucial for the success of the computer simulation.We obtained the following results :1.A novel computer simulation program running on PC was developed, and publicised in a book form.2.An upwind-type scheme along the characteristic curves was found appropriate for the condition on the open boundary. The related discussion is presented in the paper, which is submitted to a journal for publication.