Journal of Applied Mechanical Engineering

Extreme computation of Stokes flow using axial Green function method on refined axial lines

2^nd International Conference on Fluid Dynamics & Aerodynamics

October 19-20, 2017 | Rome, Italy

Do Wan Kim

Inha University, South Korea

Scientific Tracks Abstracts: J Appl Mech Eng

Abstract:

The axial Green function method (AGM) has been developed for the efficient numerical computations of the solution of partial differential equations that comes from physical phenomena, for instance, like the electric potential, the heat, the convection-diffusion, and the Stokes flow. Recent progress in AGM enables us to calculate extreme problems caused by the geometry of a domain. We refine the axial lines enough to resolve the accurate solution near the geometric extreme region of interest, and elsewhere the axial lines are coarsely distributed. This gives rise to the non-matching axial lines along the interface between the extreme and the other regions. At the non-matching points on the interface, we develop how to glue the solutions across the interface numerically. The pressure blow-up in Stokes flow is one of extreme phenomena of interest. Here, the pressure blow-up takes place between two adjacent circular bodies that are extremely close but donâ??t touch each other. Since it is fundamental to understand singular behavior of the solution in this case, we accurately calculate the blow-up pressure between close bodies to predict how serious it is. To do this efficiently, the AGM with refinement is employed. According to our calculation, the pressure blow-up becomes the reciprocal of square distance between bodies.

Biography :

Do Wan Kim has his expertise in inventing and improving the numerical methods for solving partial differential equations appearing in Physics and Engineering. His basis consists of mathematical analysis of numerical methods, FDM, FEM, Meshfree Method, and recently Axial Green function methods. Moreover, fluid structure interaction is one of his research topics. The problem solving in any area is the ultimate purpose of his research.