| Project/Area Number |
14550060
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Engineering fundamentals
|
|---|
| Research Institution | Chuo University |
|---|
Principal Investigator |
NAKAYAMA Tsukasa Chuo University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (20144446)
|
|---|
| Project Period (FY) |
2002 – 2003
|
| Project Status |
Completed (Fiscal Year 2003)
|
| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2002: ¥2,000,000 (Direct Cost: ¥2,000,000)
|
|---|
| Keywords | Computational Fluid Dynamics / Unified numerical method / Finite element method / Advection equation / Automatic differentiation / CIVA method / 特性曲線法 / 数値解析 / アルゴリズムの自動微分 |
|---|
| Research Abstract |
A unified numerical method is developed for the analysis of both compressible and incompressible viscous flows. The governing equations are the compressible Navier-Stokes equations, the equation of continuity and the energy equation expressed in terms of pressure. The temporal discretization of the governing equations is based on the finite difference method. The procedure for advancing flow field variables in a time step consists of two phases, namely an advection phase and a non-advection phase, and accordingly the governing equations are split into the advection and non-advection equations. First, the non-advection phase is calculated. The non-advection equations are discretized in space by using the Galerkin FEM based on Bercovier-Pironneau triangular elements. Those discrete equations are solved in an implicit manner to yield the intermediate values of the variables. These intermediate values are corrected by solving the advection equations. The advection equations are solved by CIVA method. CIVA method is based on the method of characteristics, which uses cubic interpolation functions. The interpolation function needs the first-order spatial derivatives of unknown variables. Those derivatives are calculated by solving the equations obtained by differentiating the governing flow equations with respect to spatial variables. The proposed method is demonstrated in two numerical examples of compressible and incompressible flows; a shock-tube problem and Poiseuille flow in a straight pipe. The accuracy of the proposed method has been assessed by comparing our numerical results with analytical solutions. Encouraging results have been obtained.
|
