Boundary data immersion method for Cartesian-grid simulations of fluid-body interaction problems

Abstract

A new robust and accurate Cartesian-grid treatment for the immersion of solid bodies within a fluid with general boundary conditions is described. The new approach, the Boundary Data Immersion Method (BDIM), is derived based on a general integration kernel formulation which allows the field equations of each domain and the interfacial conditions to be combined analytically. The resulting governing equation for the complete domain preserves the behavior of the original system in an efficient Cartesian-grid method, including stable and accurate pressure values on the solid boundary. The kernel formulation allows a detailed analysis of the method, and it is demonstrated that BDIM is consistent, obtains second-order convergence relative to the kernel width, and is robust with respect to the grid and boundary alignment. Formulation for no-slip and free slip boundary conditions are derived and numerical results are obtained for the flow past a cylinder and the impact of blunt bodies through a free surface. The BDIM predictions are compared to analytic, experimental and previous numerical results confirming the properties, efficiency and efficacy of this new boundary treatment for Cartesian grid methods.