Takafumi Makihara

Application of the GSMAC-CIP Method to Incompressible Navier-Stokes Equations at High Reynolds Numbers

The conventional shape function for the finite-element method (FEM) is linear, and it is thus inadequate for analyzing numerically complex flows at high Reynolds numbers. In this study, we propose a new scheme, GSMAC-CIP, using the third-order shape function, which requires continuity of the value of the function and its first space derivative in the whole space and is formulated by a finite element method for the cubic interpolated pseudo-particle (CIP) method. We verified the effectiveness of this new scheme by analyzing the forced-driven convection in a square cavity at Re = 1000, 5000 and 10000. The numerical results obtained by the present scheme are compared with those of GSMAC-FEM using coarser meshes, and it is shown that the present scheme is superior to GSMAC-FEM in terms of space accuracy. Moreover, it is shown that the numerical results obtained by the present scheme using fine meshes were in precise agreement with those obtained by Ghia et al.

Verification of GSMAC-CIP Method by the Flows in a Square Cavity.

The conventional shape function for the finite-element method (FEM) is a linear one, which is inadequate for analyzing numerically complex flows for high Reynolds numbers. In the present study, we propose GSMAC-CIP scheme using 3rd order shape function which requires continuity of the value of the function and its first space derivative in whole space and is formulated a finite element method for the cubic interpolated pseudo particle (CIP) method. We verified the effectiveness of this new scheme by the forced convection in a square cavity at Re=1 000, 5 000, 10 000. The numerical results obtafined by the present scheme is compared with those of GSMAC-FEM using rough meshes and it is showed that present scheme is superior to GSMAC-FEM on the space accuracy. Moreover, it is shown that the numerical results obtained by present scheme using fine meshes are agreement with those obtained by Ghia et al.

Theoretical Study on Equation of Motion and Yield Stress of Electrorheological Fluid.

The flow of ER fluid has been analyzed theoretically using the constitutive equation of Bingham fluid. However it is necessary to take account of internal rotation in ER fluid, because it is suspension containing particles. The equation of motion of ER fluid is derived using not only the constitutive equation of stress for Bingham fluid but also the micropolar electrically conducting fluids theory, assuming the equilibrium equation of angular momentum. For yield stress which is the characteristics of ER fluid, the interaction of particles which polarized by applied electric field leads us to the conclusion based on a two-body problem at the cutting surface of cluster. A theoretical equation is derived by dipole-dipole interaction. Yield stress in this study is not dynamic yield stress but static yield stress.