Layered Immersed Boundary Method for General CFD Applications

In this work, we present a novel Layered Immersed Boundary Method (LIBM) designed for general CFD applications. The proposed method overcomes the limitations of traditional immersed boundary methods by introducing immersed boundary layers that are aligned with the boundary geometry. These layers enhance resolution in the normal direction while stretching the grid in the lateral and longitudinal directions, effectively reducing computational costs. LIBM exhibits exceptional accuracy in resolving boundary layers, even at high Reynolds numbers, where conventional IBMs tend to fail or become prohibitively expensive. This makes it particularly well-suited for simulating turbulent and multiphase flows involving moving and/or morphing structures. Additionally, immersed boundary layers ensure a continuous and consistent description of the geometry which ensures the integrity of the numerical simulation and facilitates the implementation of Neumann and Robin boundary conditions. Unlike traditional direct forcing IBMs, the proposed method does not suffer from mass-conservation issues, freshly-vacated cells, and the stair-step problem since LIBM separates points of action of hydrodynamic forces from those of virtual forces. Overall, the versatility and accuracy of the LIBM make it a valuable tool for a wide range of CFD simulations, particularly those involving complex flows with intricate boundary geometries and high Reynolds numbers.