境界埋め込み法に整合するポアソン式の差分表現(流体工学,流体機械)

概要

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A finite difference formula of Poisson equation consistent with an immersed boundary method was derived in a mathematical way. In order to verify the method with this Poisson equation numerically, an LES of turbulent flow in a plane channel was carried out. This result was compared with those obtained by a traditional Poisson equation with different boundary conditions. Those were the gradient-free condition on the wall surface and the entirely uniform treatment for the scalar potential, found in existing literatures. The former decreased the accuracy of divergence-free condition at the cell adjacent to the wall, and the latter increased the mean velocity. The present method with this Poisson equation simultaneously reproduced accurate no-slip condition at the wall, divergence-free condition and mean velocity.
2004-09-25