Implicit large eddy simulation of flows around bodies of arbitrary shape on cartesian grids using a conservative immersed interface method

Abstract

This work presents an immersed interface method for representing complex boundaries in Implicit Large-Eddy Simulation on three-dimensional, staggered Cartesian Grids. The immersed obstacle in the fluid domain is characterized by a levelset field. Initial flux calculations are carried out for the entire domain in the same way. Cells intersected by the immersed interface then undergo a special treatment: only the fluid part is considered, no-slip condition and no-through-flux condition are imposed by changing the flux balance and a homogeneous Neumann condition for pressure is enforced in the pressure projection. To deal with the small cell problem a cell-mixing procedure is applied. The approach is fully conservative and we demonstrate the method is second-order accurate. The validation and the performance of the approach are done with some numerical examples of 2D and 3D flow configurations.