A novel approach for wall-boundary immersed flow simulation (proposal of modified Navier-Stokes equation)

This study proposes a novel approach for the wall-boundary immersed flow simulation, wherein the Navier-Stokes equation is modified to include a level-set definition of a solid body in fluid flow. The proposed numerical model is defined via a system of differential equations based on the law of conservation and has a continuous approximate profile near the solid body. It yields a stable viscosity solution using a simple algorithm and scheme without any upwind schemes, numerical limiters, or addition filters. The model is numerically validated via solutions of flow around a cylinder, which are consistent with theoretical and experimental results for both steady and unsteady cases based on the wide Reynolds number (Re=8–160) of laminar flow condition.