Title: Difference Formula of Poisson Equation Consistent with an Immersed Boundary Method
Abstract: 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.