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Do Wan Kim

Do Wan Kim

Inha University, South Korea

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

Biography

Biography: Do Wan Kim

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 don’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.

Recent Publications

1.W Lee, H K Kim and D W Kim (2017) Axial Green function method for axisymmetric electromagnetic field computation. IEEE Transactions on Magnetics 53(6):7206504.

2.W Lee and D W Kim (2014) Localized axial Green’s function method for the convection-diffusion equations in arbitrary domains. Journal of Computational Physics 275:390-414.

3.S Jun and D W Kim (2011) Axial Green’s function method for steady stokes flow in geometrically complex domains. Journal of Computational Physics 230:2095-2124.

4.Y Shang, Y He, D W Kim and X Zhou (2011) A new parallel finite element algorithm for the stationary Navier-Stokes equations. Finite Elements in Analysis and Design 47:1262-1279.

5.D W Kim, S K Park and S Jun (2008) Axial Green’s function method for multi-dimensional elliptic boundary value problems. International Journal for Numerical Methods in Engineering 76:697-726.