A cut-cell method for sharp moving boundaries in Cartesian grids

A cut-cell method is presented which is well suited for the simulation of viscous flows with immersed moving boundaries in Cartesian meshes. It is shown that abrupt changes in the discrete approximation close to the moving boundary generate unphysical oscillations in the solution. Such errors are avoided by using a smooth discrete formulation for cases when, e.g. new cells emerge or cells disappear due to the moving boundary. Additionally, a method is detailed which can handle multiply cut cells, which arise often in more complex three-dimensional geometries. Several test cases and applications are presented in which the boundary location is determined by a level-set method. The level-set method allows an efficient determination of the cut cell points without the necessity to compute it at each time step from the CAD data of the moving geometry. Different level set functions are used for bodies which move with different speed, such that also the opening and closing process of a valve can be resolved without the necessity of remeshing or interpolation of solutions. Results of validation test cases show the accuracy of the overall method, while the simulation of the flow in a simplified internal combustion engine demonstrates the applicability to complex flow problems.