| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2005: ¥3,000,000 (Direct Cost: ¥3,000,000)
|
|---|
| Research Abstract |
In the present study, we first carried out basic research of hybrid method of fluid-kinetic equations. We established a simple theory of high-resolution shock capturing scheme for compressible Navier-Stokes equations. This theory relies on the simple structure of characteristics of kinetic equation. The linearity of the convection term in kinetic equation drastically simplifies the theory of characteristics and the splitting of numerical flux can naturally be done. The reconstruction of fluid-dynamic variables is done via the distribution function of gas molecules, which enables the shock capturing and less dissipative nature in well-resolved region. These results are summarized as lecture notes for graduate and under-graduate students. In the problem of two dimensional jet expansion into vacuum, we demonstrated the usefulness of hybrid method. As far as the deterministic hybridization, the connection between two solutions can be done without any serious difficulties. Next, we proceeded to the study on simple numerical method for incompressible, flows based on kinetic theory. The Lattice Boltzmann method is well-known as a kinetic incompressible solver. Then, we carried out a systematic asymptotic analysis of this method and found that this method is a variant of well-known artificial compressibility method. The artificial compressibility approach is now widely believed as a tool for obtaining steady solutions. However, the systematic asymptotic analysis reveals its potential as a high order accurate solver in time-dependent case. This subject is continuously studied. As a related work, we developed an accurate numerical method for viscous Burgers equation. By making use of well-known Cole-Hopf transformation locally, we could derived an accurate formula of solution, which is expressed as a rational polynomial.
|
