2003 Fiscal Year Final Research Report Summary
Theory and appliation of microscopic approaches to macroscopic fluid-dynamic equations
| Project/Area Number |
14550150
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Fluid engineering
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
OHWADA Taku Kyoto University, Aeronautics and Astronautics, Associate Professor, 工学研究科, 助教授 (40223987)
|
|---|
| Project Period (FY) |
2002 – 2003
|
| Keywords | kinetic scheme / Navier-Stokes equations / Euler Equations / Boltzmann equation / BGK equation / Splitting Method / shock wave / boundary layer |
|---|
| Research Abstract |
In this research project, the theory of kinetic scheme for the gas-dynamic equations (compressible Euler equations, compressible Navier-Stokes equations) is established and some numerical methods are developed. The kinetic scheme, which was originally developed as a mimic of the DSMC method for the Boltzmann equation, is revealed to be an extension of the classical Lax-Wendroff scheme and the significance of the kinetic approach is shown to be in the management of the discontinuous reconstruction of the macroscopic state. The newly developed kinetic schemes, which are based on this new finding, work as shock-capturing schemes and yield fine boundary-layer profiles with reasonable resolution. These schemes can easily be applied to various molecular models; the extensions to the NS equations for hard-sphere molecules and the Euler equation for diatomic gases are made. With the oversea research collaborator, the head investigator developed kinetic schemes for the Burnett and super-Burnett equations, which deal with higher order rarefaction effects. Furthermore, a hybrid method, which solves fluid-dynamic equations in (nearly) equilibrium regions and kinetic equation in non-equilibrium regions is developed. In the course of these studies, the time step truncation error of the DSMC was studied. The outcome of this study is reflected in the construction of new schemes. Under the supervision of the head investigator, some graduate students (master) worked in this research project and had the opportunity as speakers in an international conference, which is an outcome of the present project from the educational point of view.
|
Research Products
(8 results)
