等角写像を用いて任意の2次元単連結領域に直交曲線格子を生成する一数値計算法(熱工学,内燃機関,動力など)

概要

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One easy way to numerically generate an orthogonal grid in 2D domain is presented and discussed. An orthogonal grid is generated by conformal mapping, i.e., this method finds at the same time both the regular complex function which determines mapping and the rectangular domain which is mapped to a given 2D domain. The grid lines are equal to isotherms of 2D steady heat conduction problems under certain boundary conditions, so a generated grid shape can be imagined well before computation. The formulation is really simple only using Cauchy's integral formula, a rudimentary theorem of complex analysis. Because the process is non-iterative, and the boundary integral is partly performed analytically in the formulation, computation time is short even though generating a large number of grid points. This method is not very flexible about grid spacing control, but is useful with respect to the simplicity and the potential of speedy calculation. Test calculations show that this method is successfully applied to various geometries.
2010-08-25