Numerical calculation of fully-developed laminar flows in arbitrary cross-sections using finite difference method

The finite difference method has adequate accuracy to calculate fully-developed laminar flows in regular cross-sectional domains, but in irregular domains such flows are solved using the finite element method or structured grids. However, it has become apparent that we can use the finite difference method freely even if domains are complex. The non-slip condition on the wall must be imposed. Even in irregular domains, this boundary condition can be introduced indirectly by adding a single procedure to set the boundary condition. The calculations have similar accuracy as in regular domains. The proposed method has a wide range of applications; as a first step, fully-developed laminar flows are investigated in the paper. Copyright 2011 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [doi:10.1063/1.3652881]